Mathematics

Problem

Which of the following algebraic manipulations would most directly eliminate the indeterminate form in the limit

\displaystyle\lim_{x\to 0}\dfrac{\sqrt{5+2x}-\sqrt{5}}{x}

? a) Factor an

x

out of the numerator. b) Multiply the numerator and denominator by

\sqrt{5+2x}-\sqrt5

. c) Multiply the numerator and denominator by

\sqrt{5+2x}+\sqrt5

. d) Rewrite

\sqrt{5+2x}

5+x

and simplify.