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Chapter 4: Problem 7
Give the antiderivatives of \(1 / x\)
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The velocity function and initial position of Runners \(A\) and \(B\) are given. Analyze the race that results by graphing the position functions of the runners and finding the time and positions (if any) at which they first pass each other. $$\text { A: } v(t)=\sin t, s(0)=0 ; \quad \text { B: } V(t)=\cos t, S(0)=0$$
Graph several functions that satisfy the following differential equations. Then find and graph the particular function that satisfies the given initial condition. $$f^{\prime}(x)=3 x+\sin \pi x ; f(2)=3$$
Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima. $$f(x)=x^{3}-3 x^{2}$$
Locate the critical points of the following functions. Then use the Second Derivative Test to determine (if possible) whether they correspond to local maxima or local minima. $$f(x)=6 x^{2}-x^{3}$$
Given the following acceleration functions of an object moving along a line, find the position function with the given initial velocity and position. $$a(t)=4 ; v(0)=-3, s(0)=2$$
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