_ x -2 (x^7+128 x^3+8 )= - Vidyadip

MCQ

$\lim _{x \rightarrow-2}\left(\frac{x^7+128}{x^3+8}\right)=$

A
$\frac{56}{3}$
✓
$\frac{112}{3}$
C
$\frac{121}{3}$
D
$\frac{28}{3}$

✓

Answer

Correct option: B.

$\frac{112}{3}$

(B) $\frac{112}{3}$
Hint:
$\lim _{x \rightarrow-2} \frac{x^7+128}{x^3+8} $
$=\frac{\lim _{x \rightarrow-2} \frac{x^7-(-2)^7}{x-(-2)}}{\lim _{x \rightarrow-2} \frac{x^3-(-2)^3}{x-(-2)}}$
$=\frac{7(-2)^6}{3(-2)^2}=\frac{112}{3} \quad \ldots\left[\because \lim _{x \rightarrow \mathrm{a}} \frac{x^n-\mathrm{a}^n}{x-\mathrm{a}}=\mathrm{na}^{\mathrm{n}-1}\right]$

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