Explore BrainMass

Explore BrainMass

    Calculus problems

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    30) If f(x) = ln(sin(x^2)), then f''(x)=? Explain.

    31) The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fencing? Explain.

    Ans is 20sqrtof 10 by 30sqrt of 10. explain.

    32) Let f(x) = x^3 + x. If h is the inverse function of f then h'(20) equals?
    Ans = ¼. Explain.

    33) A spherical balloon is inflated. At a rate of 25cm^3/sec. At what rate in cm/sec is the radius of the balloon changing when the radius is 2cm? Ans is 25/16pi. Explain.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:52 pm ad1c9bdddf
    https://brainmass.com/math/basic-calculus/calculus-problems-15026

    Solution Preview

    30)
    f'(x)=2x cos(x^2) / sin(x^2) = 2x cotan(x^2)
    here we can consider f(x)=h(l(m(x)) where h=ln, l=sin and m=^2 functions. Then
    f'(x)=m'(x)*l'(m(x))*h'(l(mx)) = 2x cos(x^2) / sin(x^2)
    31)
    Let's assume that the length of one side is x and the other side is y. Then xy=6000; moreover, the used fence according to the description given in ...

    Solution Summary

    This looks at derivatives, inverses, and rate of change.

    $2.49

    ADVERTISEMENT