Hyperbolic functions and their graphs Quiz

1. Which expression is equal to $\sinh x$?

• A. $\frac12(e^x-e^{-x})$
• B. $\frac12(e^x+e^{-x})$
• C. $e^x-e^{-x}$
• D. $\frac{e^x-e^{-x}}{e^x+e^{-x}}$

2. Find the exact value of $\cosh(\ln2)$.

• A. $\frac34$
• B. $\frac52$
• C. $\frac54$
• D. $\frac35$

3. Which describes the graph of $y=\tanh x$?

• A. Even, with a minimum at $(0,1)$
• B. Odd, increasing, with asymptotes $y=\pm1$
• C. Odd, with vertical asymptotes $x=\pm1$
• D. Increasing, with a single asymptote $y=1$

4. What is the limit of $\cosh x-\sinh x$ as $x\to\infty$?

• A. $1$
• B. $\infty$
• C. $\frac12$
• D. $0$

5. Solve $\cosh x=3\sinh x$.

• A. $x=\ln2$
• B. $x=\frac12\ln2$
• C. $x=\frac12\ln3$
• D. $x=0$