Define the function q(x)= cases a

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define the function q(x)={a sin⁡xx,x≠0,3,x=0.q(x)= \begin{cases} a\,\dfrac{\sin x}{x}, & x\ne 0,\\ 3, & x=0. \end{cases} Determine the value of aa that ensures lim⁡x→0q(x)\displaystyle\lim_{x\to 0} q(x) exists.

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