Mathematics

Problem

Let

g(x)=\dfrac{\sqrt{x}-5}{x-25}

, defined for

x>0

. Which of the following statements about

\displaystyle\lim_{x\to25} g(x)

is true? a) The limit is

0

because the numerator approaches

0

faster than the denominator. b) Both one-sided limits exist and equal

\dfrac{1}{10}

; therefore the limit equals

\dfrac{1}{10}

. c) The limit does not exist because the expression becomes the indeterminate form

0/0

x=25

. d) After simplification, the limit equals

\dfrac{1}{5}