Which of the following algebraic manipulations would most directly eliminate the…

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

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.