Chapter 1: Problem 69
Solve the inequality for \(x\). $$ e^{x}>5 $$
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True or False? Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(\lim _{x \rightarrow c} f(x)=L\) and \(f(c)=L,\) then \(f\) is continuous at \(c\)
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 \(f^{-1}\).
Boyle's Law For a quantity of gas at a constant temperature, the pressure \(P\) is inversely proportional to the volume \(V\). Find the limit of \(P\) as \(V \rightarrow 0^{+}\).
In Exercises \(131-134,\) sketch the graph of the function. Use a graphing utility to verify your graph. $$ f(x)=\arcsin (x-1) $$
Prove that \(\arctan x+\arctan y=\arctan \frac{x+y}{1-x y}, x y \neq 1\). Use this formula to show that \(\arctan \frac{1}{2}+\arctan \frac{1}{3}=\frac{\pi}{4}\)
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