Calculus Questions & Answers

\( \int _{}^{}(\frac{5}{\sin (^{2}x)-3x^{2}+e^{x}}) d x \)

66. Rams' Horns The average annual increment in the horn length (in centimeters) of bighorn rams born since 1986 can be approximated by \[ y=0.1762 x^{2}-3.986 x+22.68 \text {, } \] where \( x \) is the ram's age (in years) for \( x \) between 3 and 9 . Inte- grate to find the total increase in the length of a ram's horn during this time. Source: Journal of Wildlife Management. 67. Beagles The daily energy requirements of female beagles who are at least 1 year old change with respect to time according to the function \[ E(t)=753 t^{-0.1321} \text {, } \] where \( E(t) \) is the daily energy requirement (in kJ/ \( \left.W^{0.67}\right) \), where \( W \) is the dog's weight (in kilograms) for a beagle that is \( t \) years old. Source: Journal of Nutrition. a. Assuming 365 days in a year, show that the energy require- ment for a female beagle that is \( t \) days old is given by \( E(t)=1642 t^{-0.1321} \). b. Using the formula from part a, determine the total energy requirements (in kJ/ \( W^{0.67} \) ) for a female beagle between her

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by \( E^{\prime}(x)=12 x+10 \), where \( x \) is the number of days since the start of the job. Find the expenditure if the job takes 4 days. A. \( \$ 5,800 \) B. \( \$ 13,600 \) C. \( \$ 136 \) D. \( \$ 58 \)

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by \( E^{\prime}(x)=12 x+10 \), where \( x \) is the number of days since the start of the job. Find the expenditure if the job takes 4 days. A. \( \$ 5,800 \) B. \( \$ 13,600 \) C. \( \$ 136 \) D. \( \$ 58 \)

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by \( E^{\prime}(x)=12 x+10 \), where \( x \) is the number of days since the start of the job. Find the expenditure if the job takes 4 days.

Find the integral. \( \int 8 e^{4 y} d y \)

Find the general solution for the differential equation. \( \frac{d y}{d x}=12 x^{2}-10 x \)

2. \( -\lim _{x=5} \frac{4 x^{2}-2}{2 x+1} \)

\begin{tabular}{l} Question \\ Given the cost function \\ \( \qquad C(x)=2800+550 x+0.4 x^{2} \) \\ and the demand function \( p(x)=1870 \) for each item \( x \), find the production level \( x \) that will maximize profit. Your answer \\ should be the whole number that corresponds to the highest profit. \\ Provide your answer below: \\ \( \qquad \begin{array}{l}\text { P items }\end{array} \) \\ \hline\end{tabular}

63. Cell Division Let the expected number of cells in a culture that have an \( x \) percent probability of undergoing cell division dur- ing the next hour be denoted by \( n(x) \). a. Explain why \( \int_{20}^{30} n(x) d x \) approximates the total number of cells with a \( 20 \% \) to \( 30 \% \) chance of dividing during the next hour. b. Give an integral representing the number of cells that have less than a \( 60 \% \) chance of dividing during the next hour. c. Let \( n(x)=\sqrt{5 x+1} \) give the expected number of cells (in millions) with \( x \) percent probability of dividing during the next hour. Find the number of cells with a 5 to \( 10 \% \) chance of dividing. 64. Bacterial Growth A population of \( E \). coli bacteria will grow at a rate given by where \( w \) is the weight (in milligrams) after \( t \) hours. Find the change in weight of the population from \( t=0 \) to \( t=3 \). 65. Blood Flow In an example from an earlier chapter, the velocity \( v \) of the blood in a blood vessel was given as \[ v=k\left(R^{2}-r^{2}\right) \text {, } \]