Practice Exam

Question 8 • Precalculus

Function g of x has a removable discontinuity at x is equal to c , where g of c is undefined. Which statement describes the one-sided limits at x is equal to c ?

Answer

limit x to c raised to the negative power of g x DNE limit x to c raised to the plus power of g times x is equal to b [for some value b ]

limit x to c raised to the negative power of g x DNE limit x to c raised to the plus power of g x DNE

limit x to c raised to the negative power of g times x is equal to A limit x to c raised to the plus power of g times x is equal to A [for some value A ]

limit x to c raised to the negative power of g times x is equal to A limit x to c raised to the plus power of g times x is equal to b [for distinct value A and b ]

Explanation

A removable discontinuity means the function approaches the same finite value from the left and from the right, even though g(c) is undefined. Thus both one-sided limits exist and are equal to some value A. Choice C describes this; different one-sided limits, or limits that do not exist, would not be removable discontinuities.

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