Consider the function f(x)= cases x^ 2 , & x1

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

Problem

Consider the function f(x)={x2,x<1,2,x=1,x,x>1.f(x)=\begin{cases} x^{2}, & x<1,\\[4pt] 2, & x=1,\\[4pt] \sqrt{x}, & x>1. \end{cases} (i) Evaluate lim⁡x→1−f(x)\displaystyle \lim_{x\to1^-} f(x) and lim⁡x→1+f(x)\displaystyle \lim_{x\to1^+} f(x). (ii) Decide whether ff is continuous at x=1x=1. (iii) Name and justify the type of discontinuity, if any, occurring at x=1x=1. (iv) Write the largest interval or union of intervals on which ff is continuous.

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