Chapter 1: Problem 5
Find the limit. $$ \lim _{x \rightarrow-3}\left(2 x^{2}+4 x+1\right) $$
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$$ \begin{aligned} &\text { Prove that if } f \text { and } g \text { are one-to-one functions, then }\\\ &(f \circ g)^{-1}(x)=\left(g^{-1} \circ f^{-1}\right)(x). \end{aligned} $$
Use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in the interval [0, 1]. Repeatedly "zoom in" on the graph of the function to approximate the zero accurate to two decimal places. Use the zero or root feature of the graphing utility to approximate the zero accurate to four decimal places. $$ f(x)=x^{3}+3 x-3 $$
Write the expression in algebraic form. \(\sin (\arccos x)\)
Find the point of intersection of the graphs of the functions. $$ \begin{array}{l} y=\arcsin x \\ y=\arccos x \end{array} $$
Show that the function \(f(x)=\left\\{\begin{array}{ll}0, & \text { if } x \text { is rational } \\ k x, & \text { if } x \text { is irrational }\end{array}\right.\) is continuous only at \(x=0\). (Assume that \(k\) is any nonzero real number.)
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