Chapter 1.5, Problem 1C

(a)

To determine

Whether given statement is true or not.

“The limit of a difference of functions as $x\to c$ is equal to the difference of the limits of that function as $x\to c$ , provided that all limit exist.”

(b)

To determine

Whether given statement is true or not.

“If $f(x)$ is within 0.25 unit of 7 & $g(x)$ is within 0.25 unit of 2, then $f(x)+g(x)$ is within 0.5 unit of 9.”

(c)

To determine

Whether given statement is true or not.

“If $f(x)$ is within 0.25 unit of 7 & $g(x)$ is within 0.25 unit of 2, then $f(x).g(x)$ is within 0.5 unit of 9.”

(d)

To determine

Whether given statement is true or not.

“Every algebraic function ‘f’ is continuous at every real number $x=c$ .”

(e)

To determine

Whether given statement is true or not.

“Every power function $f(x)=A{x}^k$ is continuous at $x=2$ ”

(f)

To determine

Whether given statement is true or not.

“The function $f(x)=\sec x$ is continuous at $x=\frac{\pi }{2}$ ”

(g)

To determine

Whether given statement is true or not.

“The value of $\frac{(x-c)f(x)}{(x-c)g(x)}$ at $x=c$ is equal to the limit of $\frac{f(x)}{g(x)}$ at $x=c$ ”

(h)

To determine

Whether given statement is true or not.

“The value of $\frac{(x-c)f(x)}{(x-c)g(x)}$ as $x\to c$ is equal to the limit of $\frac{f(x)}{g(x)}$ as $x\to c$ ”