Science:Math Exam Resources/Courses/MATH104/December 2015/Question 10 (a)/Statement

Let $f(x)=x^{2}+x-{\frac {1}{x}}-1$. Its derivative satisfies

$f'(x)=2x+1+{\frac {1}{x^{2}}}={\frac {2x^{3}+x^{2}+1}{x^{2}}}={\frac {(x+1)(2x^{2}-x+1)}{x^{2}}}$.

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(a) Evaluate $\lim _{x\to 0^{-}}f(x)$ and $\lim _{x\to 0^{+}}f(x)$.