Let and be real numbers with

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

Problem

Let

a

and

b

be real numbers with

a\neq b

. Determine

\displaystyle\lim_{x\to 0}\dfrac{\sqrt{1+ax}-\sqrt{1+bx}}{x}

. (a)

a-b

(b)

\dfrac{a^2-b^2}{2}

(c)

\dfrac{a-b}{2}

(d)

\dfrac{b-a}{2}