1. In this exercise, we will explore how the limit laws will not apply if the point at which the two functions being considered is such that one or both of the limits of those functions do not exist. A. Find a pair of example functions f: R → R and g: R → R for which lim (f(x) + g(x)) = 0 but neither lim f(x) nor lim g(x) exists. (Hint: jumps that balance each other out?) x→2 x→2 x-2 B. Find a pair of example functions f: R → R and g: (-∞, 2) U (2, ∞)→ R for which lim f(x) = 0 the value of lim (f(x) · g(x)) equals 1. (Hint: x-2 x-2 notice the domain of function g.) C. By choosing a different function g in part B, for any real number c, we could find a pair of functions for which lim f(x) = 0 and the value of x-2 lim (f(x) · g(x)) equals c. Explain. x-2

1. In this exercise, we will explore how the limit laws will not apply if the point at which the two functions being considered is such that one or both of the limits of those functions do not exist. A. Find a pair of example functions f: R → R and g: R → R for which lim (f(x) + g(x)) = 0 but neither lim f(x) nor lim g(x) exists. (Hint: jumps that balance each other out?) x→2 x→2 x-2 B. Find a pair of example functions f: R → R and g: (-∞, 2) U (2, ∞)→ R for which lim f(x) = 0 the value of lim (f(x) · g(x)) equals 1. (Hint: x-2 x-2 notice the domain of function g.) C. By choosing a different function g in part B, for any real number c, we could find a pair of functions for which lim f(x) = 0 and the value of x-2 lim (f(x) · g(x)) equals c. Explain. x-2

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.1: Limits

Problem 9E

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