Consider the function f(x)= cases (ax) x , & x 0

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

Problem

Consider the function f(x)={sin⁡(ax)x,x≠0,k,x=0,f(x)=\begin{cases} \dfrac{\sin(ax)}{x}, & x \ne 0,\\ k, & x=0, \end{cases} where aa is a non-zero constant. Determine kk so that ff is continuous at x=0x=0.

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