The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Problems

In Problems 1-8, express Δy and dy as functions of x and Δx, and for Δx infinitesimal find an infinitesimal s such that Δy = dy + ε Δx.

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9           If y = 2x2 and z = x3, find Δy, Δz, dy, and dz.

10           If y = 1/(x + 1) and z = 1/(x + 2), find Δy, Δz, dy, and dz.

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21            Let y = √x, z = 3x. Find d(y + z) and d(y/z).

22            Let y = x-1 and z = x3. Find d(y + z) and d(yz).

In Problems 23-30 below, find the equation of the line tangent to the given curve at the given point.

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31             Find the equation of the line tangent to the parabola y = x2 at the point (x0, x02,).

32            Find all points P(x0, x02,) on the parabola y = x2 such that the tangent line at P passes through the point (0, -4).

33            Prove that the line tangent to the parabola y = x2 at P(x0, x02) does not meet the parabola at any point except P.


Last Update: 2010-11-25