Question

Solve algebraically. Formula below:

Answer 1

\[\lim_{x \rightarrow 0} \sin (4x) \over \sin(3x)\]

Answer 2

you can use l'hopital's rule.
it says when you have a case where you get 0/0 or infinity/infinity,
then you can take the first derivative of the top function and divide it by the first derivative of the bottom function.

Answer 3

Divide by the highest coff. which is x
so the answer will be 4/3

Answer 4

This was on the test yesterday. We don't know l'hospital's rule yet :(

Previous examples showed manipulating the problem so that you can use

lim x -> 0 \[\sin (x) \over x\] = 1

Answer 5

@glorydotcom : Here is the steps:
\[\huge \lim_{x \rightarrow 0} \frac{\sin4x}{\sin3x}\]
Divide by the highest coff. of x which is x^1.
\[\huge \lim_{x \rightarrow 0} \frac{\frac{(\sin4x)}{(x)}}{\frac{(\sin3x)}{(x)}}\]
=
\[\huge \frac{4}{3}\]

Answer 6

l'hospital's rule's the easiest way to do it.. and the only way i can think up right now.. ><
so the derivative of sin(4x) = 4cos(x)
and similarly, sin(3x) = 3cos(x)

when x-> 0, you get 4(1)/3(1) to get 4/3.

oh. what @Eyad did above is almost correct.
you can do that, but

sin(3x)/x doesn't simplify to 3 like that. the answer is 3, but it's not because the x's have cancelled.

Answer 7

@nuk64 :actually i didn't say anthing about canceling ,Did I ?

Answer 8

so for sin(3x)/x, what you do is multiply the top and bottom by 3.
so you do sin(3x)*3/x*3

then you get 3sin(3x)/3x which is the same property - sin(x)/x which goes to 1.
so you have 3*1 which equals 3. :)

same goes for the sin(4x).

oh. true. sorry @Eyad ><

Answer 9

@nuk64 :Nvm :) and btw good explanation :)

Answer 10

Thanks guys!