Let be the function defined by f(x)= cases 3x^2-4x+1, & x<2, [4pt] kx+5, & x 2

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

Problem

Let ff be the function defined by f(x)={3x2−4x+1,x<2,kx+5,x≥2.f(x)=\begin{cases} 3x^2-4x+1, & x<2,\\[4pt] kx+5, & x\ge 2. \end{cases} Investigate the continuity of ff at x=2x=2. (i) Find the left-hand limit lim⁡x→2−f(x)\displaystyle \lim_{x\to 2^-}f(x). (ii) Find the right-hand limit lim⁡x→2+f(x)\displaystyle \lim_{x\to 2^+}f(x). (iii) Determine the value of kk for which ff is continuous at x=2x=2.

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