Chapter 2, Problem 4PE

(a)

To determine

The value of $\underset{x\to 0}{\lim }-g(x)$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.

(b)

To determine

The value of $\underset{x\to 0}{\lim }g(x)·f(x)$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.

(c)

To determine

The value of $\underset{x\to 0}{\lim }f(x)+g(x)$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.

(d)

To determine

The value of $\underset{x\to 0}{\lim }\frac{1}{f(x)}$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.

(e)

To determine

The value of $\underset{x\to 0}{\lim }x+f(x)$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.

(f)

To determine

The value of $\underset{x\to 0}{\lim }\frac{f(x).\cos x}{x-1}$, if the $\underset{x\to 0}{\lim }f(x)=\frac{1}{2}$ and $\underset{x\to 0}{\lim }g(x)=\sqrt{2}$.