Problem 2
Differentiating Hyperbolic Functions Evaluate the following derivatives: a. \(\frac{d}{d x}\left(\sinh \left(x^{2}\right)\right)\) b. \(\frac{d}{d x}(\cosh x)^{2}\)
Problem 2
True or False? If true, prove it. If false. find the true answer. If you invest \(\$ 500\), an annual rate of interest of \(3 \%\) yields more money in the first year than a \(2.5 \%\) continuous rate of interest.
Problem 3
Integrals Involving Hyperbolic Functions Evaluate the following integrals: a. \(\int x \cosh \left(x^{2}\right) d x\) b. \(\int \tanh x d x\)
Problem 3
In the following exercises, compute each indefinite integral. $$ \int 2^{x} d x $$
Problem 3
Find \(f^{\prime}(x)\) for each function. $$ f(x)=e^{x^{3} \ln x} $$
Problem 3
Find the antiderivative of \(\int \frac{d x}{\sqrt{1-16 x^{2}}}\).
Problem 3
For the following exercises, find the derivative \(\frac{d y}{d x}\). $$ y=\frac{1}{\ln x} $$
Problem 4
Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{2}-a^{2}}, \quad a \neq 0\)
Problem 4
For the following exercises, find the indefinite integral. $$ \int \frac{d t}{3 t} $$
Problem 4
Evaluate the following integrals: a. \(\int \sinh ^{3} x \cosh x d x\) b. \(\int \operatorname{sech}^{2}(3 x) d x\)
