Let f(x) = l x^3 + x^2 - 16x + 20 (x - 2) ^2 , if ;x 2 ; ; ; ; ; … - Vidyadip

MCQ

Let $f(x) = \left\{ \begin{array}{l}\frac{{{x^3} + {x^2} - 16x + 20}}{{{{(x - 2)}^2}}},{\rm{if }}\;x \ne 2\\\;\;\;\;\;\,\;\;\;\;\;\;\;k\;\;\;\;\;\;\;\;,\;{\rm{if }}\;x = 2\end{array} \right.$ If $f(x)$ be continuous for all $x$, then $ k =$

✓
$7$
B
$-7$
C
$ \pm 7$
D
None of these

✓

Answer

Correct option: A.

$7$

a
(a) For continuous $\mathop {\lim }\limits_{x \to 2} \,f(x) = f(2) = k$

$ \Rightarrow \,\,k = \mathop {\lim }\limits_{x \to 2} \frac{{{x^3} + {x^2} - 16x + 20}}{{{{(x - 2)}^2}}}$

$ = \mathop {\lim }\limits_{x \to 2} \,\frac{{({x^2} - 4x + 4)\,\,(x + 5)}}{{{{(x - 2)}^2}}} = 7$

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