Use the power series to determine a power series for the function .  

Find the cubic function of the form where and the coefficients are real numbers, which satisfies the conditions given below. ​ Relative maximum: Relative minimum: Inflection point: ​

Suppose the deflection D of a beam of length L is , where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection. ​

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. ​ x f(x) ​

For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity. x f(x) ​

The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln. ​ ​ Find . ​

The measurements of the base and altitude of a triangle are found to be 27 and 26 centimeters. The possible error in each measurement is 0.1 centimeter. Use differentials to estimate the propagated error in computing the area of the triangle. Round your answer to four decimal places. ​

A rectangular page is to contain 36 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. ​

The graph of f is shown below. For which value of x is minimum? ​ ​

Determine whether the Mean Value Theorem can be applied to the function on the closed interval . If the Mean Value Theorem can be applied, find all numbers c in the open interval such that . ​