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Application of Derivative and Evalution of Integral

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October 6th, 2022

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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