Question

find the limit numerically in equation below, please help!!

Answer 1

\[\lim_{\theta \rightarrow 0} (\sin \theta)/\theta \]

Answer 2

sorry let me re write

Answer 3

what does "numerically" mean in this context?

Answer 4

this is a famous limit
\[\lim_{x\to 0}\frac{\sin(x)}{x}=1\]

Answer 5

\[\lim_{ \theta \rightarrow 0} (\sin3\theta)/\theta \]

Answer 6

\[\frac{\sin(3x)}{x}=\frac{3\sin(3x)}{3x}\]

Answer 7

so all you do is put the number in parentheses on outside of equation on numerator and denom?

Answer 8

i just arranged it so you can use
\[\lim_{x\to 0}\frac{\sin(3x)}{3x}=1\]

Answer 9

oh ok. so where does the one 3 that you put infront sin go? i see how the 3x cancels its self out but not the other 3

Answer 10

the 3 is still there
that makes the answer 3

Answer 11

ok so sin(3x)/3x cancels out? and all thats left is 3?

Answer 12

Yup. The important part here was how you change the sin(3x)/x into looking like a limit you know the answer to (the sin(3x)/3x) by multiplying the top and bottom by 3.

Answer 13

ok so any time you see a formula like this the answer is the number in front of theta? just show your work by making top and bottom multiplied by that number?

Answer 14

Well I am not sure if your solution would work all of the time. As long at it is the limit as x approach 0 for sin(x)/x then you know that that will equal 1 so you can set it equal to 1 and continue solving your equation if necessary.

Answer 15

What you need to do is first identify that you can change it to that format (sin(x)/x) and then do whatever multiplying is necessary.

Answer 16

I hope I am making sense here!

Answer 17

yes thanks !