If f(x) = l x^2 + 3x - 10 x^2 + 2x - 15 , ; ; when , , x - 5 , ,a… - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}\frac{{{x^2} + 3x - 10}}{{{x^2} + 2x - 15}},\;\;{\rm{when \,\,}}x \ne - 5\\\,\,a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,{\rm{when\,\, }}x = - 5\end{array} \right.$ $x = - 5$ is continuous at $x = - 5$, then the value of $'a\ '$ will be

A
$\frac{3}{2}$
B
$\frac{7}{8}$
C
$\frac{8}{7}$
D
$\frac{2}{3}$

✓

Answer

$\mathop {\lim }\limits_{x \to \, - \,5} f(x) = \frac{{(x - 2)\,\,(x + 5)}}{{(x + 5)\,(x - 3)}}$
$= \frac{{ - 7}}{{ - 8}}$
$= \frac{7}{8}.$

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