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    Calculus problems

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    12) What is limit as h approaches 0 of [cos(pi/2 + h) - cos(pi/2)] / [h]
    Ans is -1. Explain.

    14) The area of the region in the first quadrant between the graph of y=x times the
    sqrt of (4-x^2) and the x axis is? Ans is 8/3. Explain.

    15) If x^2 + y^3 = x^3y^2, then dy/dx = ? Explain.

    Ans is [3x^2y^2 - 2x] / [ 3y^2 - 2x^3y]

    16) limit as x approaches infinity of x^2/xlnx =?
    Ans is infinity? Explain.

    15) Integral of lnx/x dx. Answer is (ln x)^2/ 2 + C. Explain

    18) For which of the following functions does d^3y/dx^3 = dy/dx?
    I. y=e^x
    II. y=e^-x
    III. y=sinx

    Ans is I and II.

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    Solution Preview

    Please see the attachment.

    12) Let , we know . Thus we have

    14) Let . Set , ...

    Solution Summary

    There are a variety of problems for calculus that involve limits, integrals and area