Chapter 2.6, Problem 45E

(a) Estimate the value of

$\underset{x\to -\infty }{\lim }\left(\sqrt{x^2+x+1}+x\right)$

by graphing Use function $f(x)=\sqrt{x^2+x+1}+x$.

(b) Use a table of values of f(x) to guess the value of the limit.

(c) Prove that your guess is correct.