Problem 6
Use \(y=y_{0} e^{k t}\). If bacteria increase by a factor of 10 in 10 hours, how many hours does it take to increase by \(100 ?\)
Problem 6
Evaluate the following derivatives: a. \(\frac{d}{d x}\left(\cosh ^{-1}(3 x)\right)\) b. \(\frac{d}{d x}\left(\operatorname{coth}^{-1} x\right)^{3}\)
Problem 6
Evaluate the limit \(\lim _{x \rightarrow a} \frac{x-a}{x^{n}-a^{n}}, \quad a \neq 0\).
Problem 6
Evaluate the definite integral \(\int_{0}^{\sqrt{3} / 2} \frac{d u}{\sqrt{1-u^{2}}}\).
Problem 6
In the following exercises, compute each indefinite integral. $$ \int \frac{2}{x} d x $$
Problem 6
Find \(f^{\prime}(x)\) for each function. $$ f(x)=\frac{10^{x}}{\ln 10} $$
Problem 6
For the following exercises, find the derivative \(d y / d x\). (You can use a calculator to plot the function and the derivative to confirm that it is correct.) $$ \text { [T] } y=\frac{\ln (x)}{x} $$
Problem 7
For the following exercises, find the derivative \(d y / d x\). (You can use a calculator to plot the function and the derivative to confirm that it is correct.) $$ \text { [T] } y=x \ln (x) $$
Problem 7
Find an antiderivative of \(\int \frac{1}{1+4 x^{2}} d x\).
Problem 7
In the following exercises, compute each indefinite integral. $$ \int \frac{1}{x^{2}} d x $$
