- #1

- 76

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## Homework Statement

lim

x-o+ (tan(4x))^x

## Homework Equations

## The Attempt at a Solution

to get the derivative i have to use the chain rule so it would be.

lim

x- 0+ (x(tan(4x)^x-1)(sec^2(4)

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- Thread starter jpd5184
- Start date

In summary, the conversation discusses the use of L'Hospital's rule to find the derivative of a function involving the tangent function. The experts recommend transforming the function into a logarithmic form and using the limit of the natural logarithm to solve the problem.

- #1

- 76

- 0

lim

x-o+ (tan(4x))^x

to get the derivative i have to use the chain rule so it would be.

lim

x- 0+ (x(tan(4x)^x-1)(sec^2(4)

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- #2

- 124

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First you have to identify what kind of indeterminate form you have. Can you see you have the form

To apply L'Hospital's rule, remember that you need to have [tex]\frac{0}{0}[/tex] or [tex]\frac{\pm \infty}{\pm \infty}[/tex]. What can do you do to transform this

Good luck.

- #3

Science Advisor

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- #4

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would i just make tanx into sinx/cosx

- #5

Mentor

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For this type of problem there is a technique that is useful.

Let y = (tan(4x))

Then ln y = x ln(tan(4x)) = tan(4x)/(1/x)

Now take the limit of both sides, and recognize that what you're getting is the limit of the ln of what you want.

Check your textbook. I'm betting that there is an example that uses this technique.

- #6

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thanks very much, i did learn this technique, just forgot it.

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