Problem 1
In the following exercises, compute each indefinite integral. $$ \int e^{2 x} d x $$
Problem 1
Evaluate the following derivatives: a. \(\frac{d}{d x}\left(\tanh \left(x^{2}+3 x\right)\right)\) b. \(\frac{d}{d x}\left(\frac{1}{(\sinh x)^{2}}\right)\)
Problem 1
For the following exercises, find the derivative \(\frac{d y}{d x}\). $$ y=\ln (2 x) $$
Problem 1
Find \(f^{\prime}(x)\) for each function. $$ f(x)=x^{2} e^{x} $$
Problem 1
Evaluate the limit. Evaluate the limit \(\lim _{x \rightarrow \infty} \frac{e^{x}}{x}\).
Problem 1
The following integration formulas yield inverse trigonometric functions: \(1 .\) $$ \int \frac{d u}{\sqrt{a^{2}-u^{2}}}=\sin ^{-1} \frac{u}{a}+C $$ \(2 .\) $$ \int \frac{d u}{a^{2}+u^{2}}=\frac{1}{a} \tan ^{-1} \frac{u}{a}+C $$ \(3 .\) $$ \int \frac{d u}{u \sqrt{u^{2}-a^{2}}}=\frac{1}{a} \sec ^{-1} \frac{u}{a}+C $$
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
Evaluating a Definite Integral Using Inverse Trigonometric Functions Evaluate the definite integral \(\int_{0}^{1} \frac{d x}{\sqrt{1-x^{2}}}\).
Problem 2
In the following exercises, compute each indefinite integral. $$ \int e^{-3 x} d x $$
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.
