Problem 4
Evaluate the following integrals: a. \(\int \sinh ^{3} x \cosh x d x\) b. \(\int \operatorname{sech}^{2}(3 x) d x\)
Problem 4
True or False? If true, prove it. If false. find the true answer. If given a half-life of \(t\) years, the constant \(k\) for \(y=e^{k t}\) is calculated by \(k=\ln (1 / 2) / t\).
Problem 4
Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{2}-a^{2}}, \quad a \neq 0\)
Problem 4
Find \(f^{\prime}(x)\) for each function. $$ f(x)=\sqrt{e^{2 x}+2 x} $$
Problem 5
Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{3}-a^{3}}, \quad a \neq 0\).
Problem 5
In the following exercises, compute each indefinite integral. $$ \int \frac{1}{2 x} d x $$
Problem 5
Find the indefinite integral using an inverse trigonometric function and substitution for \(\int \frac{d x}{\sqrt{9-x^{2}}}\).
Problem 5
Differentiating Inverse Hyperbolic Functions Evaluate the following derivatives: a. \(\frac{d}{d x}\left(\sinh ^{-1}\left(\frac{x}{3}\right)\right)\) b. \(\frac{d}{d x}\left(\tanh ^{-1} x\right)^{2}\)
Problem 5
For the following exercises, find the indefinite integral. $$ \int \frac{d x}{1+x} $$
Problem 5
Use \(y=y_{0} e^{k t}\). If a culture of bacteria doubles in 3 hours, how many hours does it take to multiply by 10 ?
