Inverse trigonometric functions, L’Hopitals Rule and Integration by Parts
Please see the attached file for the fully formatted problems.
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