Q214 / 270 · NDA 2017 (Phase 2) · Mathematics

Consider the following : 1. $\mathrm{x}+\mathrm{x}^2$ is continuous at $\mathrm{x}=0$ 2. $\mathrm{x}+\cos \frac{1}{\mathrm{x}}$ is discontinuous at $\mathrm{x}=0$ 3. $x^2+\cos \frac{1}{x}$ is continuous at $x=0$ Which of the above are correct?

  • Correct answer
    A
    $1$ and $2$ only
  • B
    $2$ and $3$ only
  • C
    $1$ and $3$ only
  • D
    $1,2$ and $3$

Solution

$\mathrm{x}+\mathrm{x}^2$ is continuous at $\mathrm{x}=0$ $\mathrm{x}+\cos \frac{1}{\mathrm{x}}$ is discontinuous at $\mathrm{x}=0$ $x^2+\cos \frac{1}{x}$ is not continuous at $x=0$.

Hence, the correct answer is option: 'A'.

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