Answer to Question #87781 in Calculus for Shivam Nishad

Question

Evaluate the following limits
i) lim x→-1 (x²+3x+2)/1-x²
ii) lim x→0 (√1+x –1)/x

Answer 1

$i) \lim_{x\to -1}\frac{x^2+3x+2}{1-x^2}=\lim_{x\to -1}\frac{(x+1)(x+2)}{(1-x)(1+x)}=\lim_{x\to -1}\frac{x+2}{1-x}=\frac{-1+2}{1-(-1)}=\frac{1}{2}\\ ii) \lim_{x\to 0}\frac{\sqrt{1+x}-1}{x}=\lim_{x\to 0}\frac{(1+x)-1}{(\sqrt{1+x}+1)x}=\lim_{x\to 0}\frac{1}{\sqrt{1+x}+1}=\frac{1}{\sqrt{1+0}+1}=\frac{1}{2}$