Question

$\underset{x\to 1}{lim}\frac{x^4-3x^2+2}{x^3-5x^2+3x+1}$

Answer 1

$\underset{x\to 1}{lim}\frac{x^4-3x^2+2}{x^3-5x^2+3x+1}$ $\frac{0}{0}$ form

Using L'Hospital's rule we get,

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

$=\frac{-2}{-4}=\frac{1}{2}$.