limit x tends to 1 sin(pi x)
if I replace x=y+1
limit y tends to 0 sin pi (y+1)=sin (pi y)
#limit
haughty glade
marble parrotBOT
limit x tends to 1 sin(pi x)
if I replace x=y+1
limit y tends to 0 sin pi (y+1)=...
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haughty glade
I do not understand the last step how they can write it?
haughty glade
sin(π(y+1)) = -sin(πy)
why negative sign
flat bay
because sin(x) = -sin(x+π) for all x
haughty glade
wait a second
let me send you original post
i am arjun btw i use this account on laptop
flat bay
they put the negative sign at the front of the fraction
haughty glade
they put the negative sign at the front of the fraction
ohh
haughty glade
because sin(x) = -sin(x+π) for all x
but here it is different no?
sin pi(x)=-sin pi (y+1)?
flat bay
sin(πx) = sin(π(y+1))
which is -sin(πy)
note that sin(π(y+1)) = sin(πy + π) = -sin(πy)
adding or subtracting a π to an angle inside sin will always flip the sign
arctic sundial
i am arjun btw i use this account on laptop
...you can use the same account on multiple devices.
mystic crescent
Ok good
mystic crescent
l'hopital and seperate limits
Taylor expansion is a lot better for these types of problems imo but if you haven’t learned it yet then l’hôpital is good
alpine locust
Yes. I have learnt it
mystic crescent
You switched accounts faster than me running out of school after a long day
haughty glade
Yooo
alpine locust
Yoo
haughty glade
Yoo
alpine locust
Yoo
mystic crescent
Yes. I have learnt it
Okay well try solving it with it you’ll see how efficient it is
If you have time of course non pressure
alpine locust
But how i start with it?
mystic crescent
*no
alpine locust
Which function i expand
mystic crescent
well you know for instance that (1+t)^a=1+at+o(t) for t approaching 0
And also sin(pit) ~pit for t approaching 0
Also 4^t-1=e^2tln(2)-1~2tln(2) for t approaching 0
And let’s not forget ln(1+t/2)~t/2 for t approaching 0
Using all of these you can simplify the expression further
mystic crescent
Let me delete one
No it’s fine lol you can have two accounts if you want
alpine locust
+close
alpine locust
+close
haughty glade
+CLOSE