Let and be real numbers

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

k

and

m

be real numbers, and define

f(x)= \begin{cases} \dfrac{x^{2}-k^{2}}{x-k}, & x\neq k,\\ m, & x=k. \end{cases}

For which relationship between

m

and

k

is

f

continuous at

x=k

? (a)

m=k^{2}

(b)

m=2k

(c) There is no real number

m

that makes

f

continuous at

x=k

(d)

m=k

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