Chapter 1: Problem 94
Use a calculator to approximate the value. Round your answer to two decimal places. $$ \arctan (-3) $$
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Prove that for any real number \(y\) there exists \(x\) in \((-\pi / 2, \pi / 2)\) such that \(\tan x=y\)
Prove that if \(\lim _{x \rightarrow c} f(x)\) exists and \(\lim _{x \rightarrow c}[f(x)+g(x)]\) does not exist, then \(\lim _{x \rightarrow c} g(x)\) does not exist.
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the inverse function of \(f\) exists, then the \(y\) -intercept of \(f\) is an \(x\) -intercept of \(f^{-1}\).
Find all values of \(c\) such that \(f\) is continuous on \((-\infty, \infty)\). \(f(x)=\left\\{\begin{array}{ll}1-x^{2}, & x \leq c \\ x, & x>c\end{array}\right.\)
Write the expression in algebraic form. \(\tan \left(\operatorname{arcsec} \frac{x}{3}\right)\)
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