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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
$f(x)=\left\{\begin{array}{cl}2 x+1, & x<1 \\ 2, & x=1 \ is\\ x^2+1, & x>1\end{array}\right.$
  • A
    continuous at x= 1
  • B
    left continuous at x= 1
  • ✓
    right continuous at x =1
  • D
    none of these
✓

Answer

Correct option: C.
right continuous at x =1
(C)
$\lim _{x \rightarrow 1^{-}} f (x)=\lim _{x \rightarrow 1^{-}}(2 x+1)=3 \neq f (1)$
$\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1^{+}}\left(x^2+1\right)=2=f(1)$

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