Question

evaluate limit as x approaches zero from the right. (tan 8x)^x.

Answer 1

\[[\tan(8x)]^x=e^{\ln([\tan(8x)]^x)} \]

Answer 2

hmmmm

Answer 3

i would go right to the definition \[\large[\tan(8x)]^x=e^{x\ln([\tan(8x)])}\]

Answer 4

but what's the answer?

Answer 5

I think we need L'Hospitals Rule

Answer 6

\[e^{\lim_{x \rightarrow 0^+}x \ln(\tan(8x))}=e^{\lim_{x \rightarrow 0^+}\frac{\ln(\tan(8x))}{\frac{1}{x}}}\]

Answer 7

The answer was 1

Answer 8

very good

Answer 9

why didn't you tell me that first??

Answer 10

You have to do the work to determine the answer.