Application of Derivative and Evalution of Integral
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