For near , consider the quotient Q(x)= e^ 3x -1-3x e^ 2x -1-2x…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For

x

near

0

, consider the quotient

Q(x)=\frac{e^{3x}-1-3x}{e^{2x}-1-2x}.

(a) Verify that direct substitution of

x=0

yields an indeterminate form. (b) Determine

\displaystyle \lim_{x\to 0} Q(x)

and show all algebraic work required to arrive at the finite value.