Let . Which of the following statements about at is…
MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
Let f(x)=x−1x2−1. Which of the following statements about f at x=1 is correct?
(a) f has a removable discontinuity at x=1 because x→1limf(x) exists but f(1) is undefined.
(b) f is continuous at x=1 because, after cancelling the common factor, f(x)=x+1 implies f(1)=2.},{
(c) f has an infinite discontinuity at x=1 because ∣f(x)∣→∞ as x→1.},{
(d) f is continuous at x=1 because 1−112−1=0, so f(1)=0.}