A function is defined by the following descriptions near : • For ,

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

A function ff is defined by the following descriptions near x=2x=2: • For 0<x<20<x<2, f(x)=1(x−2)2+1f(x)=\dfrac{1}{(x-2)^2}+1. • For x>2x>2, f(x)=3x−5f(x)=3x-5. Which of the following is true about lim⁡x→2f(x)\displaystyle \lim_{x\to 2} f(x)? (a) The limit exists and equals 11. (b) The limit exists and equals ∞\infty. (c) The limit does not exist because the left-hand limit is unbounded while the right-hand limit is finite. (d) The limit does not exist because the function value at x=2x=2 is undefined.

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