Let q(x)=x^ 3 ,e^ x be defined for .

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

q(x)=x^{3}\,e^{\sqrt x}

be defined for

x\ge 0

. (a) Evaluate

\displaystyle \lim_{x\to0^{+}} q(x)

. (b) Provide a detailed justification for your result in part (a), explicitly referring to the continuity of each factor of

q

on its domain and to any applicable limit laws.