Calculus Answers

A curve is the graph of a function  if and only if NO vertical line intersects the curve more than once. true or false

Use L’Hopital’s rule to evaluate: ˆ

(a) limx→0 (1-cos^3x)/sin^2x

(b) limx→∞ (cos 1/x)^x

(c) limx→∞ x ln x/(x^2 - 1)

(d) limx→1 x ln x /(x^2 - 1)

You are designing a poster to contain 50 cm2 of printing with margins of 4 cm each at the top and bottom and 2 cm at each side. What overall dimensions will minimize the amount of paper used?

Let f be the function

f (x) = x2 − ln x,

where x > 1.

(a) Use the sign pattern for f'(x) to determine the intervals where f rises and where f

falls. (5)

(b) Determine the coordinates of the local extreme point(s). (2)

(c) Find f'' (x) and determine where the graph of f is concave up and where it is concave

down.