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Model Paper 10 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSModel Paper 101 Mark
Question
If $f(x)=\left\{\begin{array}{l}k x+5 \text {, when } x \leq 2 \\ x+1, \text { when } x>2\end{array}\right.$ is continuous at $x=2$ then $k= ?$
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Answer

For continuity left hand limit must be equal to right hand limit and value at the point.
Continuous at $x =2..$
$\text { L.H.L }=\lim _{x \rightarrow 2^{-}}(k x+5)$
$\Rightarrow \lim _{h \rightarrow 0}(k(2-h)+5)$
$\Rightarrow k(2-0)+5=2 k+5$
$\text { R.H.L }=\lim _{x \rightarrow 2^{+}}(x+1)$
$\Rightarrow \lim _{h \rightarrow 0}(2+h+1)$
$\Rightarrow 2+0+1$
$=3$
As $f(x)$ is continuous, we get
$\because 2 k+5=3$
$k=-1$

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