91Ó°ÊÓ

The given limit is$\underset{x→c}{\lim }f\left(x\right).$

The given statement "For $\underset{x→c}{\lim }f\left(x\right)$ to be defined, the function f must be defined at x = c" is false because the limit can be defined at any value ofx=c.

The given statement "We can calculate a limit of the form $\underset{x→c}{\lim }f\left(x\right)$ simply by finding f(c)" is false because for the limit $\underset{x→c}{\lim }f\left(x\right)$ the value is not just equal to f(c).

The given statement "If $\underset{x→c}{\lim }f\left(x\right)=10,$ then f(c) = 10"is false because for the limit$\underset{x→c}{\lim }f\left(x\right)=10,$then$f\left(c\right)≠10.$

The given statement " If f(c) = 10, then $\underset{x→c}{\lim }f\left(x\right)=10$" is false because for the limit $\underset{x→c}{\lim }f\left(x\right),$the value is not equal to $f\left(c\right).$

The given statement "A function can approach more than one limit as x approaches c" is false because if$\underset{x→c}{\lim }f\left(x\right)=A$and$\underset{x→c}{\lim }f\left(x\right)=B$then$A=B.$

The given statement "If $\underset{x→4}{\lim }f\left(x\right)=10,$ then we can make f(x) as close to 4 as we like by choosing values of x sufficiently close to 10" is false.

The given statement "If $\underset{x→6}{\lim }f\left(x\right)=∞,$ then we can make f(x) as large as we like by choosing values of x sufficiently close to 6" is true because the value of limit $x→6$gives infinity.

The given statement "If $\underset{x→∞}{\lim }f\left(x\right)=100,$ then we can find values of f(x) between 99.9 and 100.1 by choosing values of x that are sufficiently large" is true.