Calculus

Evaluatecal67.docx

Evaluate

limit as x rightwards arrow 0 of fraction numerator x squared over denominator e to the power of x minus x minus 1 end fraction

by applying L'Hôpital's rule.

In a shop, the revenue and the cost of a product are determined by

R left parenthesis x right parenthesis equals 22 x

and

C left parenthesis x right parenthesis equals 2 x squared plus 2 x plus 1

, respectively. If

represents the number of products, how many products should the shop sell to maximize the profit?