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Chapter 4: Problem 9
If \(F(x)=x^{2}-3 x+C\) and \(F(-1)=4,\) what is the value of \(C ?\)
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Use analytical methods to evaluate the following limits. $$\lim _{x \rightarrow 6} \frac{\sqrt[5]{5 x+2}-2}{1 / x-1 / 6}$$
Locate the critical points of the following functions and use the Second Derivative Test to determine whether they correspond to local maxima, local minima, or neither. $$h(x)=(x+a)^{4}, a \text { constant }$$
Use analytical methods to evaluate the following limits. $$\lim _{x \rightarrow \infty}\left(x^{2} e^{1 / x}-x^{2}-x\right)$$
Find the function \(F\) that satisfies the following differential equations and initial conditions. $$F^{\prime \prime \prime}(x)=672 x^{5}+24 x, F^{\prime \prime}(0)=0, F^{\prime}(0)=2, F(0)=1$$
Differentials Consider the following functions and express the relationship between a small change in \(x\) and the corresponding change in \(y\) in the form \(d y=f^{\prime}(x) d x\) $$f(x)=1 / x^{3}$$
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