How to do b
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zenith marsh
unreal oysterBOT
elfin rampart
How to do b
Jus draw all for graphs respective of their x cords
For0<=x<=2 , graph will be y=2x-x^2
zenith marsh
Jus draw all for graphs respective of their x cords
Can u show me?
elfin rampart
And same for all
I'll have to draw on paper
I'll try
@zenith marsh do u also need an explanation
zenith marsh
<@1277749854059368592> do u also need an explanation
If I don’t understand
elfin rampart
Yea, since the next graph also starts on the point 2,0
Its open on 4,0 I didn't draw
zenith marsh
Yea, since the next graph also starts on the point 2,0
What about pi
He’ll
Bloody hell
elfin rampart
Closed circle at 4,pi and then continue till infinity
elfin rampart
Correct, although I wouldn't recommend drawing the full parabola for the first part and draw the part only between 0 and 2
If its for a teacher
elfin rampart
No
elfin rampart
I can try
zenith marsh
You'll get it if you learn again, its very easy to understand
Can u teach me now. I may understand in 3min
elfin rampart
Sure, where exactly do u mess up in continuity
elfin rampart
It means that if there is a function f(x) let's say, in an interval (a,b), f(x) gives all real values for a to b, on a graph you can think of this as 'y' giving a continuous line instead of breaking at one point and starting at another
Like it was in the first question at 0,4 the graph was not continuous on that point
Visually, just think of functions as graph, continuous graphs give us lines which do not break
They could be straight or curve
If a function is said to be continuous in the domain let's say [0,1), so its continuous from point 0 to barely point 1
When we get open brackets, that means its mostly a limit
zenith marsh
I just know that they discontinuous when the limit didn’t exist
zenith marsh
If a function is said to be continuous in the domain let's say [0,1), so its con...
I seee
elfin rampart
Yea, for a function, you sometimes find right limit and then left limit and then on the point, if they're equal then its continuous
If they're diff then it means the graph changed on either side of its neighborhood
zenith marsh
If they're diff then it means the graph changed on either side of its neighborho...
Yeah
F’x and f’’x?
The first one is continuity?
elfin rampart
No, ' on a function means we differentiated it
F'(x) is diff one time
F''(x) is diff to times
elfin rampart
Did you take differentiation lessons as part of the calculus?
zenith marsh
Did you take differentiation lessons as part of the calculus?
I haven’t done the test yet, if I passed I can take advanced maths in September
But my teacher gives me homework about this and I forgot what he said to me
elfin rampart
They shouldve taught u that since they gave u a couple of questions
zenith marsh
They shouldve taught u that since they gave u a couple of questions
Maybe I was daydreaming in the class
Or they just talked about it for 10s
elfin rampart
Well for starters and in theory, you should know that all points which are differentiable are also continuous,but all points which are continuous are not necessarily diff
zenith marsh
Well for starters and in theory, you should know that all points which are diffe...
Yeah I remember that
elfin rampart
Diff a function is like finding its slope
elfin rampart
Yes
What part are u confused in
Okay see, take graph 4 on the pic u send me for an example ok? At 1,0 is it continuous or no?
zenith marsh
How can we know if the derivative exists or not
zenith marsh
Okay see, take graph 4 on the pic u send me for an example ok? At 1,0 is it cont...
No?
zenith marsh
Where is graph 4
elfin rampart
On graph 4, think of taking a limit on the graph, when limit goes to positive side of 1(on x axis) we get 2, when limit is on negative 1, we still get 2
zenith marsh
4th graph from the left
Oh I see
If it contains an open circle then it’s not continuous
elfin rampart
Yea
Now as u know derivative is slope of graph or simply on which angle the point is headed towards
On point(1,2) it is continuous but do u think it's diff?
zenith marsh
On point(1,2) it is continuous but do u think it's diff?
Idk what is that means
Differentiability
Let me google it
zenith marsh
On point(1,2) it is continuous but do u think it's diff?
Nope?
elfin rampart
Similar to continuity , does the function have same derivative in the neighborhood of points, if yes then diff
zenith marsh
Cuz that is a sharp turning point
elfin rampart
Yea that's correct
zenith marsh
Ok
elfin rampart
Do u know why tho
elfin rampart
No..
elfin rampart
Only straight standing line/parallel to y axis have slope infinity
zenith marsh
Only straight standing line/parallel to y axis have slope infinity
Oh
no..
elfin rampart
0 slope is parallel to x axis
elfin rampart
Okay, so when finding if a point diff or not, just like continuity,we check slopes on either side of the point like limits
elfin rampart
The limit didn’t exist at that point?
It does,that's why its continuous
elfin rampart
The point before 1,2 lies on which line
zenith marsh
Are we talking about 4?
zenith marsh
I don’t know the reason
The slope one is positive and one is negative
So it didn’t exist?
elfin rampart
That's fine, left limit of point 1,2 lies on the slanting line before it, do u agree?
zenith marsh
That's fine, left limit of point 1,2 lies on the slanting line before it, do u a...
Yeah
elfin rampart
Yess, the slopes are diff on the same point when we use limits, so the point has no actual slope hence its not diff
Get it?
elfin rampart
elfin rampart
Don't look at the extremes, limit means very very close to the point , so just anything except the actual point
zenith marsh
Don't look at the extremes, limit means very very close to the point , so just a...
Ok
elfin rampart
Yup correct
If we take limits on 1,2 left limit is usually 0.99999 and right limit is usually 1.00001
zenith marsh
Yeha ik that
zenith marsh
Yeah
But quadratic also have 2 slopes
One is negative and one is positive
Didn’t convinced myself lol
That the diff does exist
elfin rampart
Look at the point (1.00001,2)
When limit goes to 1.00001 slope goes to 0 correct?
zenith marsh
Yeah
elfin rampart
Take .99999 as limit and slope still goes to 0
elfin rampart
Its my pleasure