Chapter 2.4, Problem 2E

(a)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to -1^{+}}{\lim }f\left(x\right)=1$ is true or false.

(b)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 2}{\lim }f\left(x\right)$ does not exist is true or false.

(c)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 2}{\lim }f\left(x\right)=2$ is true or false.

(d)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 1^{-}}{\lim }f\left(x\right)=2$ is true or false.

(e)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 1^{+}}{\lim }f\left(x\right)=1$ is true or false.

(f)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 1}{\lim }f\left(x\right)$ does not exist is true or false.

(g)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 0^{+}}{\lim }f\left(x\right)=\underset{x\to 0^{-}}{\lim }f\left(x\right)$ is true or false.

(h)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to c}{\lim }f\left(x\right)$ exists at every c in the open interval $\left(-1,1\right)$ is true or false.

(i)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to c}{\lim }f\left(x\right)$ exists at every c in the open interval $\left(-1,1\right)$ is true or false.

(j)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to -1^{-}}{\lim }f\left(x\right)=0$ is true or false.

(k)

To determine

Find whether the statement about the function $y=f\left(x\right)$ $\underset{x\to 3^{+}}{\lim }f\left(x\right)$ does not exist is true or false.