Chapter 1.2, Problem 1C

a.

To determine

To find: Whether the statement “For $\underset{x\to c}{\lim }f\left(x\right)$ to be defined, the function $f$ must be defined at $x=c$ ”is true or false.

b.

To determine

To find: Whether the statement “the limit of the form $\underset{x\to c}{\lim }f\left(x\right)$ can be calculated simply by finding $f\left(c\right)$ ” is true or false.

c.

To determine

To find: Whether the statement “if $\underset{x\to c}{\lim }f\left(x\right)=10$ , then $f\left(c\right)=10$ ” is true or false.

d.

To determine

To find: Whether the statement “if $f\left(c\right)=10$ , then $\underset{x\to c}{\lim }f\left(x\right)=10$ ” is true or false.

e.

To determine

To find: Whether the statement “a function can approach more than one limit as $x$ approach $c$ ” is true or false.

f.

To determine

To find: Whether the statement “if $\underset{x\to 4}{\lim }f\left(x\right)=10$ , then we can make $f\left(x\right)$ as close to $4$ as we like by choosing values of $x$ sufficiently close to $10$ ” is true or false.

g.

To determine

To find: Whether the statement “if $\underset{x\to 4}{\lim }f\left(x\right)=\infty$ , then we can make $f\left(x\right)$ as large as we like by choosing values of $x$ sufficiently close to $6$ ” is true or false.

h.

To determine

To find: Whether the statement “if $\underset{x\to \infty }{\lim }f\left(x\right)=100$ , then we can find values of $f\left(x\right)$ between $99.9$ and $100.1$ by choosing values of $x$ that are sufficiently large” is true or false.