Chapter 2: Problem 22
Finding a Derivative In Exercises \(7-34,\) find the derivative of the function. $$ g(t)=\frac{1}{\sqrt{t^{2}-2}} $$
Chapter 2: Problem 22
Finding a Derivative In Exercises \(7-34,\) find the derivative of the function. $$ g(t)=\frac{1}{\sqrt{t^{2}-2}} $$
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Get started for freeGraphical Reasoning In Exercises \(81-84,\) use a graphing utility to graph the function and find the \(x\) -values at which \(f\) is differentiable. $$ f(x)=|x-5| $$
True or False? In Exercises \(125-128\) , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(y\) is a differentiable function of \(u,\) and \(u\) is a differentiable function of \(x,\) then \(y\) is a differentiable function of \(x .\)
Volume The radius \(r\) of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rates of change of the volume when \(r=9\) inches and \(r=36\) inches. (b) Explain why the rate of change of the volume of the sphere is not constant even though \(d r / d t\) is constant.
Tangent Lines Find equations of the tangent lines to the graph of \(f(x)=(x+1) /(x-1)\) that are parallel to the line \(2 y+x=6 .\) Then graph the function and the tangent lines.
Let \(f(x)=a_{1} \sin x+a_{2} \sin 2 x+\cdots+a_{n} \sin n x,\) where \(a_{1}, a_{2}, \ldots, a_{n}\) are real numbers and where \(n\) is a positive integer. Given that \(|f(x)| \leq|\sin x|\) for all real \(x,\) prove that \(\left|a_{1}+2 a_{2}+\cdots+n a_{n}\right| \leq 1\)
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