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JEE Main 201212 MayOnline
Exam
JEE Main
Year
2012
Date
12 May
Mode
Online
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2012 · 12 May · Online · Mathematics · Continuity and Differentiability

Statement 1: A function f: R arrow R is continuous at x_0 if and...

Statement 1: A function f:R→Rf: R \rightarrow R is continuous at x0x_0 if and only if lim⁡x→x0f(x)\lim _{x \rightarrow x_0} f(x) exists and lim⁡x→x0f(x)=f(x0⋅)\lim _{x \rightarrow x_0} f(x)=f\left(x_0 \cdot\right) Statement 2: A function f:R→Rf: R \rightarrow R is discontinuous at x0x_0 if and only if, lim⁡x→x0f(x)\lim _{x \rightarrow x_0} f(x) exists and lim⁡x→x0f(x)≠f(x0.)\lim _{x \rightarrow x_0} f(x) \neq f\left(x_0.\right)

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
  2. BStatement 1 is false, Statement 2 is true.
  3. CStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
  4. DStatement 1 is true, Statement 2 is false.

Correct answer

D. Statement 1 is true, Statement 2 is false.

Step-by-step solution

Statement-1 is true. It is the definition of continuity. Statement −2-2 is false.
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