# Math 28

Math 28, Winter 2021 Name: Quiz 2 Instructions: There are 4 problems. Read each problem carefully. Label answers appropriately. Show all your work. Submit your work on Canvas as a single PDF under Assignments, Quiz 2 Submission. [6] 1) Evaluate each of the following limits. x2 − 7x + 12 a) lim x→3 x−3 t t→−1 (1 + t)2 b) lim 4×2 − 1 x→∞ 9 − x2 c) lim [4] 2) Find the derivative of each of the following functions. Simplify your answers. a) f (x) = x2 − 4 x3 6 b) g(x) = √ x 1 [6] 3) Suppose f (x) = 2×2 − 3x + 1. Use the limit definition of the derivative to find f ′ (x). [4] 4) Suppose f is a piece-wise defined function, given by ( 2x + b if x ≤ 1 f (x) = 1 − 3x if x > 1 a) Find the left-hand and right-hand limits of f at x = 1. Use appropriate limit notation. b) Determine the value of b so that f is continuous at 1. Justify your answer using the definition of continuity. 2

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