If f(x) = * 20 c x^2 - 9 x - 3 ,, & if , , x 3 2x + k ,, & otherw… - Vidyadip

MCQ

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{\frac{{{x^2} - 9}}{{x - 3}}\,,}&{{\rm{if \,\,}}x \ne 3}\\{2x + k\,,}&{{\rm{otherwise}}}\end{array}} \right.$, is continuous at $x = 3,$ then $k = $

A
$3$
✓
$0$
C
$-6$
D
$1/6$

✓

Answer

Correct option: B.

$0$

b
(b) $\mathop {\lim }\limits_{x \to 3} f(x) = \mathop {\lim }\limits_{x \to 3} \frac{{{x^2} - 9}}{{x - 3}} = \mathop {\lim }\limits_{x \to 3} (x + 3) = 6$

and $f(3) = 2(3) + k = 6 + k$

$\because f $ is continuous at $x = 3$;

$\therefore $ $6 + k = 6 \Rightarrow k = 0$.

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