Question

Calculus Limit Question help please

Answer 1

\[\lim_{x \rightarrow \frac{ \pi }{ 2 }} \frac{ sinx }{ x }\]

Answer 2

have you tried to plug in?

Answer 3

Is there like a certain identity I must know about first?

Answer 4

oh ok so I can just use unit circle, let me try :)

Answer 5

1/\[\frac{ 1 }{ \frac{ 1 }{ \pi }}\]

Answer 6

so sin(pi/2) is 1
but how do you get x is 1/pi ?

Answer 7

I meant \[\frac{ 1 }{ \frac{ \pi }{ 2}}\]

Answer 8

ok great

Answer 9

which is 2/pi

Answer 10

When the function is continuous at the x number you are approaching you can just plug in

Answer 11

oh ok, yeah usually I just do that but idk why I felt a little weird with this one heheh thanks so much ^_^

Answer 12

because it had a trig function i bet

Answer 13

\[\lim_{x \rightarrow 3}\frac{\sin(x-3)}{x-3}\]
this one would be different
you cannot just plug in here

Answer 14

hehe no because the 3's in the numerator will cancel each other and leave a 0 in the numerator

Answer 15

well actually this limit would be 1
by comparing to this limit \[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1 \]
which is proved by the squeeze thm

(and no the u's don't cancel because that u above is in a function acting on it which is not a multiplier)

Answer 16

let u=x-3
then if x->3 then we have u=3-3=0
so u->0
so where we have x-3 i replace it with u
and where we have x->3 i will replace it with u->0
\[\lim_{x \rightarrow 3}\frac{\sin(x-3)}{x-3}=\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1\]
where u=x-3

Answer 17

But maybe you guys haven't mentioned \[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1 \]
but you will

Answer 18

ooohhh that's awesome ^_^ thanks

Answer 19

np
have fun with calculus :)

Answer 20

Oh I think my teacher went over it but very briefly, she didn't explain it she just told us to memorize \[\lim_{x \rightarrow o} \frac{ sinx }{ x } = 1\]

Answer 21

which is the same as the one yours right? with the u instead of the x

Answer 22

yes that is a very good limit to memorize
yep i just put u's instead of x's

Answer 23

oh ok :) thanks have a great day !

Answer 24

you too