Calculus 6th Edition

Metric International Edition

James Stewart

page 86.

55)

If $\displaystyle \lim_{x\rightarrow 1}\frac{f(x)-8}{x-1}=10$, find $\displaystyle \lim_{x\rightarrow 1}f(x)$.

57)

If $\displaystyle f(x)=x^2$ if $\displaystyle x$ is rational.

$\displaystyle =0$ if $\displaystyle x$ is irrational.

prove that $\displaystyle \lim_{x\rightarrow 0}f(x)=0$.

59)

Show by means of an example that $\displaystyle \lim_{x\rightarrow a}[f(x)g(x)]$ may exist even though neither $\displaystyle \lim_{x\rightarrow a}f(x)$ nor $\displaystyle \lim_{x\rightarrow a}g(x)$ exists.

61)

Is there a number $\displaystyle a$ such that

$\displaystyle \lim_{x\rightarrow -2}\frac{3x^2+ax+a+3}{x^2+x-2}$

exist? If so, find the value of $\displaystyle a$ and the value of the limit.