Let , defined for . Which of the following statements about is…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

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}