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Application of Derivative and Evalution of Integral

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1. find dx/dt of x= sqrt(1+cot(3t)).

2. f(x)=(x-2)^2*(x+3)^2, find the interval on which the function f(x) is increasing and decreasing. sketch the graph of y=f(x), and identify and local maximum or mininmum and golobal extrema.

3. f(x)= x^2/(x-1) sketch the graph, identify all extrema, inflection points, intercepts, and asymptotes. show concavity and any discontinuities.

4. f(x)= ln(sqrt((9-x^2)/(4+x^2))) apply laws of logarithms to simplify f(x) then find its derivative.

5. evaluate the integral log3(x)/(2x)

6. evaluate the integral sinh^6(x)*cosh(x) dx

7. evaluate the integral x^2 * sin(2x) dx

8 evaluate the indefinete integral sin^5(x) dx

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Solution Summary

The solution shows how to find the critical points, inflection points, and the extrema of the functions in detail. It also shows how to evaluate the indefinite integrals step-by-step.

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