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In Problems 18, express Δy and dy as functions of x and Δx, and for Δx infinitesimal find an infinitesimal s such that Δy = dy + ε Δx. 9 If y = 2x^{2} and z = x^{3}, find Δy, Δz, dy, and dz. 10 If y = 1/(x + 1) and z = 1/(x + 2), find Δy, Δz, dy, and dz. 21 Let y = √x, z = 3x. Find d(y + z) and d(y/z). 22 Let y = x^{1} and z = x^{3}. Find d(y + z) and d(yz). In Problems 2330 below, find the equation of the line tangent to the given curve at the given point. 31 Find the equation of the line tangent to the parabola y = x^{2} at the point (x_{0}, x^{02},). 32 Find all points P(x_{0}, x_{0}^{2},) on the parabola y = x^{2} such that the tangent line at P passes through the point (0, 4). 33 Prove that the line tangent to the parabola y = x^{2} at P(x_{0}, x_{0}^{2}) does not meet the parabola at any point except P.


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