Limits and Continuity — Quiz

Question 7 • Precalculus

Function f of x has a jump discontinuity at x is equal to 8 Which statement identifies possible one-sided limits at x is equal to 8 ?

Answer

limit x to 8 raised to the negative power of f x DNE and limit x to 8 raised to the plus power of f times x is equal to 120

limit x to 8 raised to the negative power of f x DNE and limit x to 8 raised to the plus power of f x DNE

limit x to 8 raised to the negative power of f times x is equal to 85 and limit x to 8 raised to the plus power of f times x is equal to 120

limit x to 8 raised to the negative power of f times x is equal to 85 and limit x to 8 raised to the plus power of f times x is equal to 85

Explanation

At a jump discontinuity, the left-hand and right-hand limits both exist as finite values but are not equal. Choice C gives a left-hand limit of 85 and a right-hand limit of 120, so they are unequal. In choice D the limits are equal, while choices A and B have a one-sided limit that does not exist.

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