Afellow calculus enthusiast was working through some practice problems.

they come to you asking if the following problem is correct: ∫ [(3x^2 + 1) / 2x] dx = [(x^3 + x) / x^2] + c

determine if they are correct. explain how you know if they are correct without integrating the function (i. e. find another method using calculus).

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.

Carley bought a jacket that was discounted 10% off the original price. the expression below represents the discounted price in dollars, based on x, the original price of the jacket.

Rose bought a new hat when she was on vacation. the following formula describes the percent sales tax rose paid b=t-c/c