gfauxpas
#help-36
soft zealotBOT
tranquil pine
Updating limits?
ripe jewel
yeah that was that
and
$$\frac{1}{\sqrt 5} , \mathrm dx = 2 \sec \theta \sec \theta \tan \theta , \mathrm d\theta$$
soft zealotBOT
gfauxpas
tranquil pine
This seems complex
ripe jewel
$$\int_{\arctan(1/5)}^{\arctan((t+1)/\sqrt 5} \frac{2\sqrt 5 \sec^2 \theta \tan \theta , \mathrm d\theta}{1+\tan^2 \theta}$$
hmm what happened
tranquil pine
$$\int_{\arctan(1/5)}^{\arctan((t+1)\sqrt 5} 2\sqrt 5 \dfrac{\sec^2 \theta \tan \theta , \mathrm d\theta}{1+\tan^2 \theta}$$
ripe jewel
see the problem?
soft zealotBOT
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gfauxpas
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tranquil pine
$$\int_{\arctan(1/5)}^{\arctan((t+1)\sqrt 5} 2\sqrt {5} \dfrac{\sec^2 \theta \tan \theta , \mathrm d\theta}{1+\tan^2 \theta}$$
soft zealotBOT
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ripe jewel
$$\int_{\arctan(1/5)}^{\arctan((t+1)\sqrt 5)} 2\sqrt 5 \dfrac{\sec^2 \theta \tan \theta , \mathrm d\theta}{1+\tan^2 \theta}$$
there we go!
soft zealotBOT
gfauxpas
ripe jewel
okay ill skip the rest but
you see how to do it now
in the simple case of
$$\int_0^t \dfrac{\mathrm dx}{x^2 + 1}$$
soft zealotBOT
gfauxpas
tranquil pine
Ooh
ripe jewel
you get arctan(t) exactly
tranquil pine
Cool
Btw
Do u have any tips fo integration?
For*
Solving methods as well as tricks if u know any
School level is enough yk
ripe jewel
just, look at a lot of different approaches so youre exposed to new techniques
wanton crater
so i was doing this
i solved it and i tried to check my answer but the derivative calculator says its wrong
final saddleBOT
so i was doing this
i solved it and i tried to check my answer but the derivati...
lusty seal
I mean
twin
just include one x inside the square root
what do we get
include 3x
lime crest
arcsech(3x)🥀
magic coyote
Welcome to mathcord Licht! 
lusty seal
x multiplied by 3x sqrt (1/9x^2 - 1) = x sqrt(1-9x^2)
lusty seal
Welcome to mathcord Licht! <:MenheraFingerGuns:998717580837666907>
hehe ty twin
fellow tensura enthussiast
lusty seal
so any idea why does it say theyre not equivalent [think](https://cdn.discordapp...
Well
shrewd nexus
x multiplied by 3x sqrt (1/9x^2 - 1) = x sqrt(1-9x^2)
its -1x^2 not -1
lusty seal
the calculator us tweaking
lusty seal
its -1x^2 not -1
check
wanton crater
i tried wolfram too but it also gave some weird form
lusty seal
x^2 is outside the square root
lusty seal
i tried wolfram too but it also gave some weird form
your answer and the calculator
wanton crater
ok so the answer i got is correct then ya?
lusty seal
both sre right
lusty seal
ok so the answer i got is correct then ya?
Yes
wanton crater
ok i was like triplechecking cuz it was just basic product rule i thought
ok ty thats all then
.close
final saddleBOT
soft zealotBOT
!
final saddleBOT
Available help channel!
final saddleBOT
vital crag
,calc sqrt(17)^2 + (4 * sqrt(17))^2
soft zealotBOT
Result:
289
,calc 17^2
soft zealotBOT
Result:
289
riemann
vital crag
,tex .double angle
soft zealotBOT
riemann
vital crag
i see yes you did
vital crag
oh we helped you cheat on your test? nice
final saddleBOT
oh we helped you cheat on your test? nice
terse crypt
riemann got manipulated ):
ripe jewel
criz might have meant that he used the server to study for the test
terse crypt
having prior knowledge regarding the exam's content is cheating
ripe jewel
idk the context so ill step out
faint edge
The thing they were asking about was definitely already graded so cheating on that seems hard.
sage meteor
studying is doubting your potential 
terse crypt
studying is doubting your potential <:eeveethink:601029006418116608>
exactlyyy
final saddleBOT
tranquil pine
Hello 
agile nacelle
This channel is closed. Please claim an open one.
tranquil pine
Okay
final saddleBOT
Available help channel!
kindred cove
final saddleBOT
kindred cove
<@&286206848099549185>
uncut flint
dont ping helpers immediately
lusty seal
😭
tribal jackal
!15mins
final saddleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
wicked mortar
Frr
tepid narwhal
<@&286206848099549185>
if you need to turn degrees you have to divide that pi
and basically numerator should be 180 degrees
kindred cove
if you need to turn degrees you have to divide that pi
what?
tepid narwhal
[Your number]* (180 degree/pi)
kindred cove
14*180degrees/pi ?
tribal jackal
14/9 * 180/pi
tepid narwhal
14/9 * 180/pi
your pi..
tribal jackal
$\frac{14\pi }{9}*\frac{180}{\pi}$
soft zealotBOT
Sarin
kindred cove
huh?
tepid narwhal
so that degrees cancels out
tired walrus
@kindred cove do you know how to do unit conversions generally?
like between m and km, or minutes and seconds, or feet and inches
tepid narwhal
$280 degrees \cdot \frac{pi}{\180i}$
tired walrus
\cdot for multiplication btw
tepid narwhal
yea
tribal jackal
.close
kindred cove
.close
final saddleBOT
tepid narwhal
is .close
sour zealot
!occupied
final saddleBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
patent rune
😢ok
steep nest
patent rune
thx both of you
final saddleBOT
Available help channel!
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nocturne cedar
I thought this was gonna be easy until I saw F wasn’t completing a triangle
severe verge
ABCD is a parallelogram?
nocturne cedar
Yes
severe verge
find the value of x?
ornate flower
How do you have EB ?
severe verge
notice that DF is the height of the parallelogram dropped from D
there's no need for pythagoras here
nocturne cedar
How do you have EB ?
First I did Pythagoras on ADE then I know DC =AB so I just subtracted
nocturne cedar
notice that DF is the height of the parallelogram dropped from D
Hm?
severe verge
do you notice the idea?
nocturne cedar
U mean DE
severe verge
DE and DF are both heights of the parallelogram
nocturne cedar
How
severe verge
it's just they have different bases
severe verge
yeah
severe verge
there's a simple idea here we can use
what is the formula for area of a parallelogram?
nocturne cedar
Idk I haven’t memorized that but I probably should
severe verge
you really should
nocturne cedar
Oh it’s really simple
severe verge
otherwise this is gonna get a little complex with similar triangles and stuff
severe verge
alr now you should be able to find x easily
severe verge
yeah
nocturne cedar
Dang
Does that means rectangles have 2 different heights too?
And triangles
Some
severe verge
triangles have 3
nocturne cedar
Not all right
An equilateral one has 1 height
Well 3 heights with the same value
severe verge
they have 3 but they have the same length
severe verge
yea switching between heights and bases is what they use to torture 5th graders here
nocturne cedar
Where do you live
severe verge
vietnam
nocturne cedar
Wdym switching between heights and bases
severe verge
exactly
nocturne cedar
Lowkey isn’t even hard I just didn’t know about the concept
severe verge
nocturne cedar
Gonna need a translation
Even with translation I can’t do it though so
Save your fingers
😔
severe verge
severe verge
no problem
nocturne cedar
.close
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
quasi plume
property of even functions
dang yeah I never learned that
rocky tusk
$\int_{-a}^a f(x) \dd{x} = 2\int_0^a f(x) \dd{x}$
soft zealotBOT
knief
soft zealotBOT
knief
rocky tusk
yea
final saddleBOT
gray ocean
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
9 - x² da y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi 12 (x4 - 19x2 - 14x + 32 9 - x² y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (X4 - 19x2 - 14x + 32) dx19 V = x -x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) 9 - x² produce y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx19 V = x [-x-12 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V = π12 (x4-18x² + 81) - (x² + 14x + 49) dx V = pi / 12 (x4 - 19x2 - 14x + 32) dx 19 V = x [-x-12x3-7 y = x + 79 - x² = x + 7 x = 1 y x = -2 V = π112 (9-x2) ² - (x + 7) 2dx V =230
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coral wedge
anyone know how even functions work on a table?
final saddleBOT
anyone know how even functions work on a table?
coral wedge
This table for example
coral wedge
|x| yields the same f(x)
okay so x values always give same y value, signs don’t change
uncut flint
yeah because its symmetrical
coral wedge
and then for odd funcs it’s just both signs flip?
uncut flint
f(-x)=f(x)
uncut flint
and then for odd funcs it’s just both signs flip?
yea f(x)=-f(x)
coral wedge
f(-x)=f(x)
all that this means is if u put in -x u have same result as u would for x
uncut flint
wait inthibk i weotr that wrong
uncut flint
all that this means is if u put in -x u have same result as u would for x
yes thats even
coral wedge
yea f(x)=-f(x)
and then this f(-x)=-f(x)?
coral wedge
okayy
dapper hull
$odd: f(-x)=-f(x) , even: f(-x)=f(x)$
soft zealotBOT
qimmah
coral wedge
got ittt, that’s what I thought it was
And then just apply this same idea when given tables
or ig it’s just visual on tables
uncut flint
yup
dapper hull
yes and in graphs
evens are symmetric along the y-axis
whilst odds are symmetric along the origin
coral wedge
yes and in graphs
evens are symmetric along the y-axis
whilst odds are symmetri...
so just look for a 180 rotation in odds?
dapper hull
so just look for a 180 rotation in odds?
yes
final saddleBOT
final saddleBOT
Available help channel!
dapper hull
Just want work checked
final saddleBOT
Just want work checked
soft zealotBOT
qimmah
dapper hull
Just want work checked
btw in the third integral i wrote 1+a^2 instead of (1+a)^2 by mistake
edgy mauve
Seems correct
Last line-closing bracket is missing
dapper hull
Seems correct
Last line-closing bracket is missing
integrating techniques be messin me up
thanks
.close
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edgy mauve
@dapper hull
Did u consider 1/(1+a)² as v?
dapper hull
<@602270020193484810>
Did u consider 1/(1+a)² as v?
no dv
edgy mauve
Why tho
dapper hull
Why tho
idk felt like it
felt the integral of ln(a) is a little messy for the working
dapper hull
Yeah got it
just did it and alna-a is in the f'g integral lol
edgy mauve
Wdym
dapper hull
simply it made things messier
edgy mauve
Well it did make me confused
But that step was cool
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hollow hedge
im baacckkk
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hollow hedge
how do i do this?
doesnt look too hard im just confused where on the line i plot the points
anyone know how these work?
deep condor
doesnt look too hard im just confused where on the line i plot the points
match up the x values with the endpoints. then use the function to find the y values at these endpoints
hollow hedge
wait do i have to do real math or can i just read the formulas and plot points
deep condor
yes, the math you are doing is over the real numbers so it's real math
hollow hedge
no i mean do i have to solve equations or are the answers in the formula
deep condor
sorry. no equations, just subbing in the x-values into the proper part of the function
hollow hedge
how do i know what formula is what line
second is the straight line im assumiung
first is red?
deep condor
second is the straight line im assumiung
makes sense, because straight lines are constants
hollow hedge
idk what the square root means thats whats confusing
deep condor
well, look at the slope of the red and blue lines
out of x^3 and sqrt(x), which do you think would have the steeper slope? i.e. which one increases quicker?
hollow hedge
i might just get it wrong and get a new question
i only have 1 attempt and im not confident at all
deep condor
i think you've nearly got this one, if you're not sure i can walk you through it a bit
hollow hedge
tbh i have to do this whole module in one day and ive literally done 7 hours of math so far
my brain is cooked
its hard to think
i have 2 more units to do and i have 2 hours
and the next unit is so complex its nauseating
deep condor
my advice would be to take a break, let the math simmer in the back of your mind, then hopefully your intuition will be a little better to finish it off
but idk your life and im not your dad
hollow hedge
i cant i just took an hour and a half break and 2 hours for 2 units is cutting close on the place i have been on
so just explain things more indepth and laymans term-like i guess
not trying to trauma dump my day lol just need a little more help
deep condor
no fair enough
these functions are elementary enough that i'll just show you some, hang on
hollow hedge
i just dont understand what each section of the formula correlates too
for the line one do i put it flat on negative 2?
deep condor
yes, flat, because it's a constant line
if you had -2x, it can vary in height, because x is a variable
deep condor
i just dont understand what each section of the formula correlates too
the red one is x^3, and the blue one is sqrt(x)
hollow hedge
are red and blue right?
if you make purple flat thats my best attempt
BRO I HAD THE WHOLE THING RIGHT AND BLUE IS ONE POINT OFF
fuck math
hollow hedge
it like follows a line
deep condor
red looks correct, but your blue starts at 2 instead of 4
hollow hedge
yea i got it wrong sadly
deep condor
oh that helps
yeah, because x >= 4, your sqrt(x) line should start at 4
does sqrt(x) include the endpoint, and why?
hollow hedge
idk what u mean
yea honestly its just hard to think with that many variables right now
i like step 1 2 3 kinda math
deep condor
the endpoint on sqrt(x) (the blue), is that included or not?
hollow hedge
yea blue was supposed to be 4
hollow hedge
yea if they are holo or whole
but ik thats if its equals to or not
i have to predict what this looks like
deep condor
but ik thats if its equals to or not
ok W just checking
i think it would be best to mess around with this graph first and get a feel for which lines are which
oh i forgot constant lines. eh you know them
hollow hedge
yea its not helpful i think im using it wrong
im on a time crunch
i got it qright
my fucking mortal enemy
what do i do if its just x < 0
this ones more complicated ngl
3 is purple
do i start on 0?
is it infinity
dense badge
what’ the value of x^2-2 when x=0?
hollow hedge
-2?
dense badge
So you know the red parabola has the open endpoint at (0,-2)
deep condor
yea its not helpful i think im using it wrong
hollow hedge
closed to include -2
dense badge
hollow hedge
huh
tiny barn
open end point is just hollow circle that implies that point is not included
dense badge
now what is the minimum y value, x^2-2 can take
tiny barn
bro i really want to just give u the answers since ur so tight on time LMAO
tiny barn
not correct
hollow hedge
which ones wrong
dense badge
parabolla ok, but blue and purple should not overlap
hollow hedge
is purple right?
tiny barn
no
hollow hedge
kinda educated guess on blue
tiny barn
im just gonna explain piecewise fucntions to u lmk if u dont understand
so you know how the functions are f(x), and f(x) is just a y value that you get after plugging a x value in
hollow hedge
wtf do i do when its not giving me 2 points
tiny barn
basically in your case the problems are giving you some ez functions to plot piecewise funcions, what u r doing is just plotting the actual functions except, on the right of the functions there is a domain, which is the restriction of the given functions
hollow hedge
lwk might just get this wrong its been 20 minutes and im not any closer
tiny barn
so simple words u r just plotting the functions in the giving restriction and erasing it if its not inside the domain
just draw the function in the domain, and deterine if endpoints are included by looking at inequality sign
hollow hedge
i have 2 end points and only 1 number
thats all im confused about atm
i appreciate the help
tiny barn
so for example f(x) = 1 just means y=1, so its just a horizontal line, and the domain is x>4, so u r just plotting y=1 starting at x = 4 and its going to the right cuz its increasing
tiny barn
so for example f(x) = 1 just means y=1, so its just a horizontal line, and the d...
^ does this make sense
hollow hedge
is that not what purple is rn?
tiny barn
and its not included because x is greater than 4 and not greater and equals to 4
hollow hedge
or is purple supposed to be blue
hollow hedge
im so lost what do i do with the other point then
tiny barn
like its in between the x-values 0 to 4, its supposed to be greater than 4 so it starts at 4 and goes to the right cuz x coordinate starts increasing going to the right
just drag it off the scren im assuming...
tiny barn
@dense badge am i getting something wrong its just f(x)=1 starting at x=4 going to the right forever no?
hollow hedge
now what do with purple
dense badge
no you good
dense badge
i’m just not a fast typer
tiny barn
point not included because its not greater AND equals, its just greater
hollow hedge
i did that
hollow hedge
x+1 0<x<4
hollow hedge
x+1 is slope?
hollow hedge
yes
tiny barn
its not just x+1, its f(x)=x+1 and only "exists" between 0 and 4
dense badge
it’s x+1 for the interval [0,4]
tiny barn
yes
hollow hedge
tiny barn
and the points are included because x can be equal to 0 and 4
hollow hedge
correct?
dense badge
almost
tiny barn
look at inequality sign
and blue is NOT included
because it will not be equal to 4
cuz x>4 not x>=4
dense badge
what’s x+1 when you plug x=0?
hollow hedge
dense badge
bingo
tiny barn
💀
tiny barn
blud next time just wait for us to finish typing
is there next problem? u dont have muhc time left right
dense badge
what’s x^2-2 at x=-1?
tiny barn
what’s x^2-2 at x=-1?
he finished the problem and got it wrong already 💀 hes showing the answer key to us
hollow hedge
tiny barn
this one is ez if u undestood what i was saying to u just compare the graphs
hollow hedge
is it b
tiny barn
i can give u a hint look at the y interceptss
hollow hedge
bc 2x-3 is slope and y
tiny barn
bc 2x-3 is slope and y
thats right answwer but gimme a better explanation than this
cuz idk wut u r trying to say
hollow hedge
uh -3 is the y and 2x is the slope
and the other 4 are wrong for that line
process of elimination
tiny barn
yes -3 is the y intercept
hollow hedge
rut row
dense badge
start with the constant function
tiny barn
try it first so we can help u
tiny barn
which one do u think is the NOT striaght line of the 3
tiny barn
whats the domain
hollow hedge
-2?
dense badge
check the end points
hollow hedge
its either -1,-1 1,1 0,0
tiny barn
and u get the right y-values by plugging the x values
hollow hedge
1,1?
tiny barn
idk what ur trying to say
hollow hedge
dense badge
what’s -x^3 when x=-2?
hollow hedge
best attempt
tiny barn
go do the other 2 first they r slightly easier
dense badge
again you can’t have overlap the function f(x) can only spit out one output for each x input
tiny barn
best attempt
ok then just chill for a sec and let us explain
i dont htink u r listening u r just placing random stuff on the graph, think abt the domain first, which x-values does the graph "exist"/reside in
hollow hedge
all the lines i placed i used like basic logic its not like im just guessing at random
dense badge
tiny barn
think abt which x-values they start at
dense badge
this say f(x) outputs x+2 when x is less than -2
hollow hedge
x+2 is the slope and the y intercept thats why purple is where it is and 3 is the y so its straight so i just slapped it on 3
thats the way im thinking about it
im 8 hours into this math session my brain is soup its hard to understand new concept
try to explain it
just anxious asf i planned on being done with this 20 minutes ago
im for sure not finishing both in time
tiny barn
you will finish on time if the rest r just easy equation algebra solving problems dw its just hard to help with grpah plotting problems without drawing
x+2 is equation, u draw it starting at x=-2 and it goes to the left because its values r smaller than -2
is this part ok?
tiny barn
beacuse it tells u x < -2
dense badge
the graph of f(x), the curve you try to draw is the set of points of the form (x,f(x))
here f(x) is defined by part meaning different range of x different procedure to get the output
so for x<-2 f(x) is computed by adding 2 to x
tiny barn
so for x<-2 f(x) is computed by adding 2 to x
x<-2
just look at this graph u r just drawing the shaded area
dense badge
so for x<-2 f(x) is computed by adding 2 to x
so for instance if x=-3 f(x)=-3+2=-1 is on the curve
hollow hedge
it shouldnt be this diffivcult
tiny barn
its fine i undestand u r like low on time and youve been wokring for too long so just try to do as fast as u can and finish so u can take a break
dense badge
the time constraint is impeding you from understanding sadly
hollow hedge
its like IXL it resets you if you get it wrong
i just wanted to watch the video explanation and it reset me
i didnt even get to answer
tiny barn
ok just skip it for now then ig and do this one
dense badge
hollow hedge
honestly this makes me feel like i have down syndrome like i take upper division classes and destroy them and then this shit kills me
its so frustrating
92 in anatomy and i cant do graphs
tiny barn
allg u r just stressedcuz ur running out of time
tiny barn
looks good
hollow hedge
im doing inverse functions
well
idk why but the inverse function unit was 4 questions
I have 50 minutes to slay this fucking titan
explain away i have time now
hollow hedge
this is the last question
tiny barn
u will definitely efel better
dense badge
bro wants closure
tiny barn
yes which is y i want our explanation to actually make sense to u
hollow hedge
ok
dense badge
what’s f(4)?
tiny barn
welcomeback
tiny barn
purple starting point is good and endpoint is correct
however your slope is not correct
whats the slope of f(x)=x+2?
dense badge
easy fix: blue not high enough
tiny barn
its 1/1 because x is not getting multiplied by any number
hollow hedge
oh mb i meant to put it on 3
attempt 2
is it right?
i refuse to lose progress atp
hollow hedge
sweet
thank you
longest 9 hours of my whole life omg
im gonna play the game and destroy my cart now
.close
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tiny barn
w closure
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fresh basin
the answer says each triangle is 1/4 of the square but without assuming that the top vertex is at the centre of the square how would we figure that out?
final saddleBOT
the answer says each triangle is 1/4 of the square but without assuming that the...
inner acorn
well it is not assuming that the top vertex is the center
it can be proved that the top vertex IS the center
fresh basin
it can be proved that the top vertex IS the center
how do we do that?
inner acorn
um, kinda hard to explain without drawing
fresh basin
um, kinda hard to explain without drawing
could you draw it :>
inner acorn
the thing is, if you can prove that so example this triangle is a 90,45,45 triangle, then it is easier to see
fresh basin
the thing is, if you can prove that so example this triangle is a 90,45,45 trian...
ohh wait it bisects that corner right
fresh basin
i think i get it
inner acorn
yeah
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mortal moat
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tranquil pine
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tranquil pine
there's a hint
but how can i find the radical axis of these 2 circles
maybe i constructed it wrong because we need AQ' to be tangent to the circle Q'RS
idk im confused
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
fiery bluff
but how can i find the radical axis of these 2 circles
Do you know the radical axis of intersecting circles?
novel kettle
im not getting any real solutions for x
final saddleBOT
im not getting any real solutions for x
novel kettle
yeah
robust mulch
oh wait i didnt flip the sign on the log term
yeah i looked on wolframalpha and it has no real sols
novel kettle
damn
robust mulch
maybe the question writer wanted a - instead of a + before the log
novel kettle
hmm
that gives me cbrt(10000)
but the options are 100, 10, 1 and 1/sqrt(10)
they probably made a mistake somewhere else im not gonna dwell on it
thanks
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fossil plaza
given the function f(x,y)= from the image above for x,y /= 0,0
and f(x,y)=0 for x,y=0
study its continuity
novel kettle
the usual argument when discussing continuity is to take limits at the problematic points (in this case, x = y = 0)
if any limit where x,y approaches 0,0 equals f(0,0), then the function is continuous
fossil plaza
ok
novel kettle
since this is in two dimensions, you don't have a "left hand limit" and a "right hand limit"
there's infinitely many ways (x,y) can approach (0,0)
novel kettle
you either have to find a counterexample where the limit doesn't equal f(0,0) (i.e. the function is discontinuous)
or prove that it equals f(0,0) for every limit (i.e. the function is continuous at that point)
fossil plaza
how do i prove it for every limit
uneven python
Along x axis , it's 0
novel kettle
you need epsilon-delta
novel kettle
as in approaching from every possible angle?
uneven python
what about polar
Polar
Mhm
Well if along line it's 0
Then ofc polar!?
I mean you could take r costheta and r sintheta
But what next?
fossil plaza
as in approaching from every possible angle?
x=costheta
y=sintheta
uneven python
R tends to 0?
novel kettle
that's still not enough, you also need to prove it for paths that are not a straight line
uneven python
Uh wait
novel kettle
like y = x^2
uneven python
that's still not enough, you also need to prove it for paths that are not a stra...
Along the line it's zero
fossil plaza
so the only way is eplsion delta ?
uneven python
Y = mx try
novel kettle
yep
uneven python
so the only way is eplsion delta ?
I'm interested in your polar suggestion
mellow iris
Along y again 0
that undefined
novel kettle
this isn't sufficient
fossil plaza
Something like this I'm doing
the denominator is r^2
uneven python
uneven python
the denominator is r^2
I was in middle of writing
fossil plaza
yeah sorry
fossil plaza
this is what i did too but i do not know if it is correct
uneven python
Then limit exists fr
novel kettle
this isn't enough to say that the limit exists
uneven python
Function must be continuous at (0,0)
uneven python
this isn't enough to say that the limit exists
Why can't you?
novel kettle
let's take another function as an example
g(x,y) = 1 if y = x^2 and 0 otherwise
uneven python
At f(0,0) it is 0 right?
novel kettle
what's the limit of this function as (x,y) approaches (0,0)?
uneven python
@fossil plaza you have the answer?
fossil plaza
of what ?
fossil plaza
let's take another function as an example
g(x,y) = 1 if y = x^2 and 0 otherwise
if you are talking about this then no
uneven python
By my method you could absolutely say that the function is continuous at origin
novel kettle
what's the limit of this function as (x,y) approaches (0,0)?
by your method, this limit exists
but it doesn't
uneven python
We had (r,theta) → 0
fossil plaza
i mean it is a singularity but the limit does exist
novel kettle
if you approach it along any straight line path, the limit is 0
but if you approach it along y = x^2, the limit is 1
so the limit doesn't exist for the function i gave as an example
fossil plaza
ohh i see than that is correct
uneven python
The function is bounded to go zero bro
Go along y = 0 path
Then limit is zero
Go along x
Still zero
But in this
We can't bound the function
But with my method
The function goes zero as it is bound
novel kettle
uneven python
|f(x,y)| ≤ r² → 0
novel kettle
my point is you can't make a conclusion just by testing every straight line path
novel kettle
i'm not talking about the original function
uneven python
Oh
uneven python
|f(x,y)| ≤ r² → 0
As r → 0
This is absolutely correct tho
Since the function is bound
novel kettle
you need to use epsilon-delta if you want that to be rigorous
uneven python
Idk what 8k doing wrong
Bro but what's wrong with my method?
Wait then
Let's try epsilon delta
novel kettle
the limit of f(x,y) as (x,y) approaches (a,b) is L if and only if
for every epsilon > 0
there exists a delta > 0
such that if 0 < |f(x,y) - L| < epsilon
then 0 < |(x,y)-(a,b)| < delta
this is epsilon-delta
if you can prove this for L = 0 and (a,b) = (0,0), then f(x,y) is continuous at (0,0)
uneven python
0 < √x²+y² < epsilon
novel kettle
that's for delta
epsilon is the upper bound for the distance between the function's value and the limit
novel kettle
other way around; 0 < |f(x,y) - L| < epsilon should imply 0 < |(x,y)-(a,b)| < delta
fossil plaza
.close
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blissful zenith
Help
blissful zenith
I used another definition for topology generated by a basis, though I found myself more clear with it but I am unsure if my current approach is correct and whether it’s more clearer
It felt more constructive this way
final saddleBOT
@blissful zenith Has your question been resolved?
summer lynx
.
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summer lynx
Im getting this as (tan theta)/2
And not tan (theta/2)
Nah im getting getting either of those
How do we get tan theta/2 here?
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round cedar
hey, i think im supposed to use the intermediate value theorem but im not sure about that
final saddleBOT
hey, i think im supposed to use the intermediate value theorem but im not sure a...
round cedar
any hint will be wonderful
but just hint not full ans
btw i made g(x)=f(x)+x and ik its continous between [-1,1]
round cedar
can i just say that becuz of IVT there must be a g(0)..? i think it aint much
meager mirage
Kinda
terse crypt
we have to prove that there exist g(x) that is positive and negative
civic sable
No information on its monotonie?
round cedar
can i just say that becuz of IVT there must be a g(0)..? i think it aint much
so i thought abt this
cuz 0 is between [-1,1]
terse crypt
And you need to prove g has to be zero within -1 to 1
well g is in between -2 and 2
-1 <= x <= 1
-1 <= f(x) <= 1
-2 <= g(x) <= 2
meager mirage
by just doing graphs i see it must have g(0)
Just check g(x) at endpoints
And use IVT
round cedar
f(x) could be 1 when x is -1
yep
terse crypt
-1 <= x <= 1
-1 <= f(x) <= 1
-2 <= g(x) <= 2
but this is still true, no?
meager mirage
but this is still true, no?
That's one case
terse crypt
this is all the cases
stray sierra
but this is still true, no?
Actually not.
civic sable
Just check g(x) at endpoints
This works fine
meager mirage
this is all the cases
Nope
meager mirage
This works fine
Yeah
terse crypt
Actually not.
if u consider all possible g max(g(x)) is 2 and min(g(x)) = -2
round cedar
Just check g(x) at endpoints
can you explain a lil bit
meager mirage
can you explain a lil bit
You know ivt right
civic sable
can you explain a lil bit
Calculate g(1) and g(-1)
Try to deduce something from that
stray sierra
if u consider all possible g max(g(x)) is 2 and min(g(x)) = -2
Yeah, if we consider all possible cases.
terse crypt
Yeah, if we consider all possible cases.
so whats wrong 
terse crypt
Actually not.
.
round cedar
f(x) could be 1 when x is -1
@terse crypt sothen i cant assume that there must be g(c)<0 g(a)>0 for example and then say that g has a root by IVT
meager mirage
<@1008702346307575818> sothen i cant assume that there must be g(c)<0 g(a)>0 for...
You can but not for that specific case
That case sorts it out by itself
round cedar
but g cant be always positive or negative cuz then there was no g(0)
civic sable
Calculate g(1) and g(-1)
Did you do this?
round cedar
Did you do this?
yep not sure what to do with that..
civic sable
yep not sure what to do with that..
alright so you have g(-1) = f(-1) -1
round cedar
yeh and g1 = f1 +1
round cedar
-1 <= f(-1) <= 1
ok g(1) must be positive and g(-1) must be negative is it right
gg then
tranquil pine
,,\int \frac{3}{(1-x)(1+x^2)},dx
final saddleBOT
,,\int \frac{3}{(1-x)(1+x^2)}\,dx
soft zealotBOT
!
tranquil pine
,,3=\frac{A}{1-x}+\frac{Bx+c}{1+x^2}
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!
sage meteor
what "help" do you need exactly?
tranquil pine
And i got $A=B=C=\frac{3}{2}$
sage meteor
seems like you know what to do
soft zealotBOT
!
tranquil pine
My ans is diff from book
tranquil pine
seems like you know what to do
Ye
sage meteor
what answer did you get? (i'm too lazy to infer)
soft zealotBOT
tranquil pine
Ye
sage meteor
which there is but
tranquil pine
Its const is 3/2
sage meteor
integrals give you a family of curves
tranquil pine
We multiply num and denom by 2
sage meteor
they could have different forms
tranquil pine
So we take 3/4 as common get that extra 2 in square of 1-x
sage meteor
the answer here is the correct answer
why do you say that your answer doesn't match when you haven't solved it
sage meteor
okay sure
be sure not to miss any algebraic manipulation stuff
that could lead to an incorrect solution
tranquil pine
Have u read previous msgs?
stuck juniper
Ohh
terse crypt
,w integrate 3/[(1-x)(1+x^2)] dx
soft zealotBOT
terse crypt
lets check the decom
tranquil pine
I got +2
scarlet sequoia
How do u get -2 😭
it depends on if you're working in (-infinity,1) or (1,infinity)
you need log|x-1| anyway
scarlet sequoia
if you're working in (1,infinity)
tranquil pine
Uhh nothing is specified like that yk
terse crypt
oh ic ic
scarlet sequoia
But book is 1-x
(x-1)^2 = (1-x)^2
so as long as you keep that square
you're fine
tranquil pine
So mines right?
scarlet sequoia
we'll check the coeffs you got
final saddleBOT
scarlet sequoia
yeah
integral of 1/(1-x), as we said
is - integral of 1/(x-1)
which is -log|x-1|
so -log(1-x) if you have x < 1
stuck juniper
Yes
scarlet sequoia
check back that
-log(1-x) differentiates into - (-1)/(1-x) = 1/(1-x)
(derivative of log u = u'/u)
tranquil pine
.reopen
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scarlet sequoia
What cant integral of 1/1-x be as it is
integral is supposed to be the "inverse" of derivative
you need to come up with a function that IS the derivative of your original integrand
so when you tell me that 1/(1-x) integrates into log(1-x)
allow me to have my doubts
tranquil pine
Ooh ye
tranquil pine
Ye i got it noe
Now*
Ye i have one more like dis
,,\int \frac{\cos x}{(1-\sin x)(2-\sin x)}, dx
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@vital kelp Has your question been resolved?
cyan kayak
@vital kelp I might be wrong, but if I'm recalling my group theory right, then {5^2 * 7^2, 3^2 * 5 * 7} is isomorphic to {3^2, 5, 5^2, 7, 7^2} by the Chinese Remainder Theorem, and similarly {3^2 * 5^2 * 7, 5 * 7^2} is also isomorphic to {3^2, 5, 5^2, 7, 7^2}. So 1 and 2 are isomorphic. However 1 and 3 are not, because {3, 3} is not isomorphic to {3^2}.
Sure, notice that 1 had a subgroup of order 9, but 3 does not.
They're both isomorphic to the same group {3^2, 5, 5^2, 7, 7^2}
by decomposition via the chinese remainder theorem
yes, and this is what I did
{5^2 * 7^2, 3^2 * 5 * 7} = Z_{5^2 * 7^2} x Z_{3^2 * 5 * 7} = Z_{5^2} x Z_{7^2} x Z_{3^2 * 5 * 7}
Z_{5^2} x Z_{7^2} x Z_{3^2 * 5 * 7} = Z_{5^2} x Z_{7^2} x Z_{3^2} x Z_{5} x Z_{7}
= {3^2, 5, 5^2, 7, 7^2}
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shrewd yew
final saddleBOT
final saddleBOT
shrewd yew
i just figured out what i did wrong while rereading it 😭 😭 😭
dapper hull
i just figured out what i did wrong while rereading it 😭 😭 😭
it's alright at least you got it on your own 😭