Question

Determine the limit

Answer 1

\[\lim x-> 0 \frac{ 3\sin4x }{ \sin3x }\]

Answer 2

sorry that's limit approaching zero lol

Answer 3

so do u know the basic limit of sin x/x =... ?

Answer 4

yes it's = 1?

Answer 5

so, according to that formula , u need the denominator same as angle of sin.
so, multiply and divide by 4x in numerator and
multiply and divide by 3x in denominator

Answer 6

\(\huge \lim \limits_{x-> 0} \frac{ 3 \frac{4x.\sin4x}{4x} }{ 3x.\frac{\sin3x}{3x} }\)

Answer 7

That seems like a bit of overkill hart :o don't you just need 4x/4x?

Answer 8

yeah, thats correct, but i wanted to brig out the point that whenever you see sin ax , multiply and divide by ax

Answer 9

well can i bring out what's in the denominator first?

Answer 10

by multiplying the denominator by 3?

Answer 11

\[\large \lim_{x \rightarrow 0}\frac{4x}{4x}\frac{3\sin4x}{\sin3x} \quad = \quad 4\lim_{x \rightarrow 0}\frac{\sin4x}{4x}\frac{3x}{\sin3x}\]

Answer 12

Oh ok i see what you meant :)

Answer 13

The upside down one will also give you 1 swin.

Answer 14

It might make more sense if you look at the way hart wrote it out.

Answer 15

yeah, lim x->0 x/sin x also equals 1

Answer 16

chyea I'm trying to find a quicker way to solve for my final hahaha! i initially split them up so it was 3sin4x/1 * 1/sin3x. I'm not sure if that's legal

Answer 17

yeah, its legal step, but you will still need the form sin x/x
so you need to multiply and divide by the angle of sin

Answer 18

So it will be 4?

Answer 19

\[\large \color{green}{Good}\quad \color{blue}{job!}\]

Answer 20

Lol thanks guys!! A couple of hours till I take my final :)

Answer 21

Oooo exciting! :O keep cramming. Sleep is good also.

Answer 22

do u need to show steps ?

Answer 23

because if you do, while taking the limit, you also need to show that
3x->0 and 4x-> 0

Answer 24

Probably not, because I think it's just simplifying it to make sinx/x = 1. But I understand how you solved it, Thanks for the review :)

Answer 25

ok, welcome ^_^