91Ó°ÊÓ

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. (Do not solve, just identify the type.) \(y^{\prime}=0.4 y(0.01-y)\)

Integration by parts often involves finding integrals like the following when integrating \(d v\) to find \(v\). Find the following integrals without using integration by parts (using formulas 1 through 7 on the inside back cover). Be ready to find similar integrals during the integration by parts procedure. $$ \int e^{-0.5 t} d t $$

Approximate each integral using trapezoidal approximation "by hand" with the given value of \(n\). Round all calculations to three decimal places. $$ \int_{0}^{1} e^{-x^{2}} d x, \quad n=4 $$

Integration by parts often involves finding integrals like the following when integrating \(d v\) to find \(v\). Find the following integrals without using integration by parts (using formulas 1 through 7 on the inside back cover). Be ready to find similar integrals during the integration by parts procedure. $$ \int(x+3)^{4} d x $$

7-42. Find each integral by using the integral table on the inside back cover. $$ \int \frac{1}{9-x^{2}} d x $$

Evaluate each limit (or state that it does not exist). $$ \lim _{b \rightarrow \infty}(3+\ln b) $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=x+y $$

Find the general solution of each differential equation or state that the differential equation is not separable. If the exercise says "and check," verify that your answer is a solution. $$ y^{\prime}=x y-1 $$

Determine the type of each differential equation: unlimited growth, limited growth, logistic growth, or none of these. (Do not solve, just identify the type.) \(y^{\prime}=6 y\)

Evaluate each limit (or state that it does not exist). $$ \lim _{b \rightarrow \infty}\left(2-\ln b^{2}\right) $$