Calculus 1 Hour Exam 1 - Math 220 Fall, 2010

1.	Given that f(x) = 2x^3 + 5, find a formula for f ^-1(x). Answer: f ^-1(x) = [(x – 5)/2 ]^1/3
2.	Suppose f(x) = 2 – ln x and g(x) = √x . Determine a formula and find the domain for ( g of f) (x) i.e. g(f(x)) Answers: g(f(x)) = √( 2 – ln x) Domain ( 0, e^2]
3.	Which one of the following equations must hold in order for a function f to be continuous at a number a? a. lim f(x) = a b. lim f(x) = 0 c. lim f(x) = f(a) xà0 xà0 xà0 d. lim f(x) = f’(a) e. lim f(x) = a f. lim f(x) = 0 xà0 xàa xàa g. lim f(x) = f’(a) h. lim f(x) = f’(a) i. lim f(x) = a xàa xàa xà∞ j. lim f(x) = f(a) k. lim f(x) = f(a) l. lim f(x) = f’(a) xà∞ xà∞ xà∞ Answer: g
4.	Given a function f(x) for which lim [ f(-5 + h) – f(-5)] / h exists, which one of the following statements must be true? a. f is continuous but not differentiable at x = -5 b. f is differentiable but not continuous at x = -5 c. f is both continuous and differentiable at x = -5 d. f is neither continuous nor differentiable at x = -5 e. f is continuous but not differentiable at x = 0 f. f is differentiable but not continuous at x = 0 g. f is both differentiable and continuous at x = 0 h. f is neither continuous nor differentiable at x = 0 i. f is continuous but not differentiable at x = 5 j. f is differentiable but not continuous at x = 5 k. f is both differentiable and continuous at x = 5 l. f is neither continuous nor differentiable at x = 5 Answer: c Click here to continue with this exam.

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