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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f (x)=\left\{\begin{array}{c}x^2 ; \text { when } x \leq 1 \\ x+5 ; \text { when } x>1\end{array}\right.$, then
  • A
    $f (x)$ is continuous at $x=1$
  • ✓
    $f (x)$ is discontinuous at $x=1$
  • C
    $\lim _{x \rightarrow 1^{+}} f(x)=1$
  • D
    $\lim _{x \rightarrow 1^{-}} f(x)=6$
✓

Answer

Correct option: B.
$f (x)$ is discontinuous at $x=1$
(B)
$\lim _{x \rightarrow 1^{-}} f (x)=\lim _{x \rightarrow 1} x^2=1$
$\lim _{x \rightarrow 1^{+}} f (x)=\lim _{x \rightarrow 1}(x+5)=6$
$\therefore \quad f (x)$ is discontinuous at $x=1$.

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