MATH 180 Study Guide - Final Guide: Classification Of Discontinuities, Quotient Rule, Product Rule
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Which are jump discontinuities? (b) determine the limit at each removable discontinuity. (c) determine the left and right limits at each jump discontinuity. y. Problem 2 solution: evaluate the following limits, or show they do not exist. (a) lim x . 3 cos(x + ) x2 4 x 2. 2 x 5 x 9 (b) lim x 2 (c) lim x 9. Solution: (a) the function f (x) = 3 cos(x + ) is continuous at x = . In fact, f (x) is continuous at all values of x in the interval ( , ). Therefore, we can evaluate the limit using substitution. lim x . 3 cos(x + ) = 3 cos( + ) = 3 cos(2 ) = 3 (b) the function f (x) = is continuous at x = 2. In fact, f (x) is continuous for all x 6= 2.
