Question

lim of squar root of x squared plus 3x plus 4 over x cubed plus 1

x approaches -1

Answer 1

Reasoning depends on the reading of the question. In both cases, the limit does not exist:

$$\lim\limits_{x\rarr -1-0}\sqrt{\frac{x^2+3x+4}{x^3+1}} \text{does not exist},\\ \lim\limits_{x\rarr -1+0}\sqrt{\frac{x^2+3x+4}{x^3+1}}=\infin,\\ \lim\limits_{x\rarr -1}\frac{ \sqrt{x^2+3x+4}}{x^3+1}=\frac{\sqrt {2}}{0}=\infin.$$