Mathematics

Mathematics

Problem

Let

f(x)=\begin{cases} x^{2}+a, & x<1\\ ax+1, & x\ge 1 \end{cases}

Which of the following statements about the limit

\displaystyle\lim_{x\to 1}f(x)

is true? a) The limit exists only if

a=0

. b) The limit exists only if

a=1

. c) The limit exists for every real value of

a

. d) The limit never exists for any real value of

a

."

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