The graph of has an open circle at and a filled dot at

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The graph of y=f(x)y=f(x) has an open circle at (2,3)(2,3) and a filled dot at (2,5)(2,5). On both sides of x=2x=2, the curve approaches the open circle smoothly. Which statement best describes ff at x=2x=2? (a) ff is continuous at x=2x=2 because lim⁡x→2f(x)\displaystyle\lim_{x\to2}f(x) exists (b) ff is not continuous at x=2x=2 because f(2)f(2) does not exist (c) ff is not continuous at x=2x=2 because f(2)≠lim⁡x→2f(x)f(2)\neq\displaystyle\lim_{x\to2}f(x) (d) ff is continuous at x=2x=2 because lim⁡x→2−f(x)=lim⁡x→2+f(x)\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2^+}f(x)

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