EXAMPLE 5 Express 1/(1 − x)2 as a power series by differentiating the equation below. What is the radius of convergence? 1 1 − x = 1 + x + x2 + x3 + = [infinity] xn n = 0 |x| < 1 SOLUTION Differentiating each side of the equation, we get 1 (1 − x)2 = 1 + Correct: Your answer is correct. + 3x2 + = [infinity] n = 1 . If we wish, we can replace n by n + 1 and write the answer as 1 (1 − x)2 = [infinity] n = 0 . According to this theorem, the radius of convergence of the differentiated series is the same as the radius of convergence of the original series, namely, R = .

What values of c and d make the equation true?

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

Dakota earned $7.50 in interest in account a and $18.75 in interest in account b after 15 months. if the simple interest rate is 4% for account a and 5% for account b, which account has the greater principal? explain. to make it a little easier, there is an image. good luck!