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# Inverse trigonometric functions, L'Hopitals Rule and Integration by Parts

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1. Prove that d/dx (csc^-1 x) = - (1 / x(square root x^2 - 1)

2. Find the derivative of the function. Simplify where possible.

y = tan^-1 (x/Q) + ln (square root (x-Q)/(x+Q))

3. Find the limit using l'Hopital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hopital's Rule does not apply, explain why.

lim x-> infinity (x - ln x)

4. Use a graph to estimate the value of the limit. Then use l'Hopital's Rule to find the exact value.

lim x -> pi/4 (tan X)^(tan2x)

5. Evaluate the integral

integral x^2 cos mx dx

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#### Solution Summary

Inverse trigonometric functions, L'Hopitals Rule and Integration by Parts are investigated in this solution. The answer is provided in an attached Word file and uses step by step calculations and graphing methods.

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