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PART - 2 CH - 12 Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPART - 2 CH - 12 Limits and Derivatives2 Marks
Question
If $f(x)=\left\{\begin{array}{ll}2 x+3, & x \leq 2 \\ 3 x+K, & x>2\end{array}\right.$ and $\lim _{x \rightarrow 2} f(x)$ are exist, then calculate the value of $K.$
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Answer


$\begin{array}{l}\text { L.H.L. }=\lim _{h \rightarrow 0} 2(2-h)+3=7 \\\text { R.H.L. }=\lim _{h \rightarrow 0} 3(2+h)+K=6+K\end{array}$
As $\lim _{x \rightarrow 2} f(x)$ exists,
$\therefore \quad$ $\text {L.H.L. = R.H.L.}$
$\therefore \quad 7=6+K$
$\quad \quad \text {K} =1$

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