Question

Evaluate : ${lim}_{x-1}\frac{x^7-2x^5+1}{x^3-3x^2+2}$

Answer 1

$\underset{x\to 1}{lim}\frac{x^7-2x^5+1}{x^3-3x^2+2}$

on differentiating both numertor & denomitator w.r.t x we get

$\Rightarrow \underset{x\to 1}{lim}\frac{\frac{d}{dx}(x^7-2x^5+1)}{\frac{d}{dx}(x^3-3x^2+2)}$

$\Rightarrow \underset{x\to 1}{lim}\frac{7x^6-10x^4}{3x^2-6x}$

on putting limit we get

$\Rightarrow \frac{7(1{)}^6-10(1{)}^4}{3(1{)}^2-6(1)}$

$\frac{7-1}{3-6}$

$=\frac{-3}{-3}$ $=1$

Hence $\underset{x\to 1}{lim}\frac{x^7-2x^5+1}{x^3-3x^2+2}$

$=1$

Hence $\underset{x\to 1}{lim}\frac{x^7-2x^{5}1}{x^3-3x^2+2}=1$.