Chapter 1.6, Problem 1C

(a)

To determine

Whether given statement is true or false.

‘If $f(x)\to 0^{+}$ then $\frac{1}{f(x)}\to \infty$ ’

(b)

To determine

Whether given statement is true or false.

‘If $f(x)\to {\infty }^{+}$ then $\frac{1}{f(x)}\to 0^{+}$ ’

(c)

To determine

Whether given statement is true or false.

‘If a limit initially has an intermediate form, then it can never be solved. ’

(d)

To determine

Whether given statement is true or false.

‘A limit ‘does not exist’ if there is no real that it approaches’

(e)

To determine

Whether given statement is true or false.

‘As limits form, ${\infty }^2\to \infty$ ’

(f)

To determine

Whether given statement is true or false.

‘As limits form, $2^2\to \infty$ ’

(g)

To determine

Whether given statement is true or false.

‘As limits form, $\infty -\infty \to 0$ ’

(h)

To determine

Whether given statement is true or false.

‘The limit of a function as $x\to c$ is always equal to the value $f(c)$ , provided that $f(c)$ exists ’