Chapter 7.3, Problem 77E

a.

To determine

To explain: Whether the statement $\frac{d}{dx}\left(\sinh \left(\ln 3\right)\right)=\frac{\cosh \left(\ln 3\right)}{3}$ is true or false.

b.

To determine

To explain: Whether the statement $\frac{d}{dx}\left(\sinh x\right)=\cosh x\text{ and }\frac{d}{dx}\left(\cosh x\right)=-\sinh x$ is true or false.

c.

To determine

To explain: Whether the statement $\ln \left(1+\sqrt{2}\right)=-\ln \left(-1+\sqrt{2}\right)$ is true or false.

d.

To determine

To explain: Whether the statement ${\displaystyle {\int }_0^1\frac{dx}{4-x^2}}=\frac{1}{2}\left({\coth }^{-1}\frac{1}{2}-{\coth }^{-1}0\right)$ is true or false.