91影视

Use \(y=y_{0} e^{k t}\). You are trying to thaw some vegetables that are at a temperature of \(1^{\circ} \mathrm{F}\). To thaw vegetables safely, you must put them in the refrigerator, which has an ambient temperature of \(44^{\circ} \mathrm{F}\). You check on your vegetables 2 hours after putting them in the refrigerator to find that they are now \(12^{\circ} \mathrm{F}\). Plot the resulting temperature curve and use it to determine when the vegetables reach \(33^{\circ} \mathrm{F}\).

For the following exercises, find the definite or indefinite integral. $$ \int_{2}^{e} \frac{d x}{x \ln x} $$

In the following exercises, find each indefinite integral by using appropriate substitutions. $$ \int e^{\tan x} \sec ^{2} x d x $$

Evaluate the limits with either L'H么pital's rule or previously learned methods. $$ \lim _{x \rightarrow 0} \frac{\sin x-\tan x}{x^{2}} $$

Use logarithmic differentiation to find \(\frac{d y}{d x}\). $$ y=\left(x^{2}-1\right)^{\ln x} $$

Evaluate the limits with either L'H么pital's rule or previously learned methods. $$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{x} $$

In the following exercises, find each indefinite integral by using appropriate substitutions. $$ \int e^{\ln x} \frac{d x}{x} $$

For the following exercises, find the definite or indefinite integral. $$ \int_{2}^{e} \frac{d x}{x \ln x} $$

Use logarithmic differentiation to find \(\frac{d y}{d x}\). $$ y=x^{\cot x} $$

Find the derivatives of the given functions and graph along with the function to ensure your answer is correct.[T] \(\frac{1}{\cosh (x)}\)