Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1. d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0.    e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5.

Question

Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0.

c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1.

d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0. 

 

e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5. 

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Math
Calculus

Limits