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Differentiation of Derivatives — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsDifferentiation of Derivatives2 Marks
Question
Find the value of $k$ for which the function.
$
f(x)=\left\{\begin{array}{cc}
\frac{x^2+3 x-10}{x-2}, & x \neq 2 \\
k, & x=2
\end{array}\right.
$
is continuous at $x=2$.
✓

Answer

$\lim _{x \rightarrow 2} f(x)=f(2)=k$
$\lim _{x \rightarrow 2} \frac{(x+5)(x-2)}{x-2}=k \quad(x \neq 2)$
$\therefore \quad k=7$.

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