Answer
a. $-\sqrt 2$
b. $\frac{\sqrt 2}{2}$
c. $\frac{1}{2}+\sqrt 2$
d. $2$
e. $\frac{1}{2}$
f. $-\frac{1}{2}$
Work Step by Step
Given $\lim_{x\to 0}f(x)=1/2$ and $\lim_{x\to 0}g(x)=\sqrt 2$
a. $\lim_{x\to 0}(-g(x))=-\sqrt 2$
b. $\lim_{x\to 0}g(x)f(x)=\sqrt 2\times\frac{1}{2}=\frac{\sqrt 2}{2}$
c. $\lim_{x\to 0}(f(x)+g(x))=\frac{1}{2}+\sqrt 2$
d. $\lim_{x\to 0}\frac{1}{f(x)}=2$
e. $\lim_{x\to 0}(x+f(x))=0+1/2=\frac{1}{2}$
f. $\lim_{x\to 0}\frac{f(x)cos(x)}{x-1}=\frac{1/2cos0}{0-1}=-\frac{1}{2}$
