Inverse hyperbolic functions Quiz

1. Which inverse hyperbolic function is defined only for $-1<x<1$?

• A. $\operatorname{arsinh}x$
• B. $\operatorname{arcosh}x$
• C. $\operatorname{artanh}x$
• D. All of them

2. Find the exact value of $\operatorname{arsinh}\frac{5}{12}$.

• A. $\ln\frac{5}{12}$
• B. $\ln\frac32$
• C. $\ln\frac{17}{12}$
• D. $\ln\frac{13}{12}$

3. Find $\operatorname{artanh}\frac12$ exactly.

• A. $\ln3$
• B. $\frac12\ln2$
• C. $\ln\frac32$
• D. $\frac12\ln3$

4. Evaluate $\int\frac{1}{\sqrt{x^2+16}}\,dx$.

• A. $\operatorname{arsinh}\frac x4+c$
• B. $\operatorname{arcosh}\frac x4+c$
• C. $\operatorname{arsinh}\frac x{16}+c$
• D. $\frac14\operatorname{arsinh}\frac x4+c$

5. Which substitution simplifies $\int\frac{1}{\sqrt{x^2-25}}\,dx$ for $x>5$?

• A. $x=5\sinh u$
• B. $x=5\cosh u$
• C. $x=25\cosh u$
• D. $x=5\tanh u$