MCQ
Function $f(x)=\left\{\begin{array}{c}x+\lambda, \text { if } x<3 \\ 4, \text { if } x=3 \\ 3 x-5, \text { if } x>3\end{array}\right.$, is continuous at $x=3$, then value of $\lambda$ is :
- ✓1
- B2
- C3
- D4
✓
Answer
Correct option: A.
1
(A)value of function at $x=3$
$
f(3)=4
$
value of L.H.L.$
\lim _{x \rightarrow 3^{-}} f(x)=\lim _{h \rightarrow 0} f(3-h)=\lim _{h \rightarrow 0}[3-h+\lambda]=3+\lambda
$because function is continuous.$
\therefore f(3)=\lim _{h \rightarrow 0} f(3-h) \quad \therefore 4=3+\lambda
$
$
\lambda=1
$
Hence correct option is (A).
$
f(3)=4
$
value of L.H.L.$
\lim _{x \rightarrow 3^{-}} f(x)=\lim _{h \rightarrow 0} f(3-h)=\lim _{h \rightarrow 0}[3-h+\lambda]=3+\lambda
$because function is continuous.$
\therefore f(3)=\lim _{h \rightarrow 0} f(3-h) \quad \therefore 4=3+\lambda
$
$
\lambda=1
$
Hence correct option is (A).
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