How do I get the value of the limit in this question (Regarding calculus- limits)

Question

Use a table of values to estimate the value of the limit (correct to three decimal places). If you have a graphing device, use it to confirm your result graphically.

lim sin(7θ)/tan(2θ)

θ->0

I'm not sure how to solve this problem since it has sin and tan. So, could you show me the process and the answer to this problem specifically? Thank you.

Answer 1

To get the limit using a table of values you would have to do something like this:

desmos.com/calculator/eytnrnglpn

Not sure if you have learned L'Hospital's rule yet? But if so you can calculate the limit manually.

sin(7x)/tan(2x) as x->0 is an indeterminate form so the "rule" can be applied (taking the derivative of the numerator divided by the derivative of the denominator gives a function that will have the same limit as the original:

7cos(7x)/2sec²(x) has a limit that looks like this (as x goes to 0):

7(1) / 2(1) = 7/2 (which is the same value that the table values are approaching in the Desmos graph).