Question

use the graphs to evaluate each quantity below. give an exact answer if a limit is a number. otherwise, enter -∞ or ∞ if a limit is infinite, or enter dne if a limit does not exist in another way.
a. as x approaches 1 from the left, f(x)+g(x) approaches
b. as x approaches 1 from the right, f(x)+g(x) approaches
c. f(1)+g(1)=
d. as x approaches 2 from the left, f(x)+g(x) approaches
e. as x approaches 2 from the right, f(x)+g(x) approaches
f. f(2)+g(2)=

Explanation:

Step1: Analyze left - hand limit at $x = 1$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to1^{-}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step2: Analyze right - hand limit at $x = 1$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to1^{+}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step3: Evaluate at $x = 1$

Find the values of $f(1)$ and $g(1)$ from the graphs and add them.

Step4: Analyze left - hand limit at $x = 2$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to2^{-}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step5: Analyze right - hand limit at $x = 2$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to2^{+}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step6: Evaluate at $x = 2$

Find the values of $f(2)$ and $g(2)$ from the graphs and add them.

Since the graphs are not provided, we cannot give numerical answers. But the general process for each part is as described above.

If we assume we had the graphs:
a. We would find $\lim_{x\to1^{-}}f(x)+\lim_{x\to1^{-}}g(x)$.
b. We would find $\lim_{x\to1^{+}}f(x)+\lim_{x\to1^{+}}g(x)$.
c. We would find $f(1)+g(1)$.
d. We would find $\lim_{x\to2^{-}}f(x)+\lim_{x\to2^{-}}g(x)$.
e. We would find $\lim_{x\to2^{+}}f(x)+\lim_{x\to2^{+}}g(x)$.
f. We would find $f(2)+g(2)$.

Since no graphs are given, we cannot provide specific numerical answers. But the steps to solve each part are as shown.

Answer:

Step1: Analyze left - hand limit at $x = 1$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to1^{-}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step2: Analyze right - hand limit at $x = 1$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to1^{+}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step3: Evaluate at $x = 1$

Find the values of $f(1)$ and $g(1)$ from the graphs and add them.

Step4: Analyze left - hand limit at $x = 2$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to2^{-}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step5: Analyze right - hand limit at $x = 2$

Look at the graphs of $f(x)$ and $g(x)$ as $x\to2^{+}$. Find the values that $f(x)$ and $g(x)$ approach and add them.

Step6: Evaluate at $x = 2$

Find the values of $f(2)$ and $g(2)$ from the graphs and add them.

Since the graphs are not provided, we cannot give numerical answers. But the general process for each part is as described above.

If we assume we had the graphs:
a. We would find $\lim_{x\to1^{-}}f(x)+\lim_{x\to1^{-}}g(x)$.
b. We would find $\lim_{x\to1^{+}}f(x)+\lim_{x\to1^{+}}g(x)$.
c. We would find $f(1)+g(1)$.
d. We would find $\lim_{x\to2^{-}}f(x)+\lim_{x\to2^{-}}g(x)$.
e. We would find $\lim_{x\to2^{+}}f(x)+\lim_{x\to2^{+}}g(x)$.
f. We would find $f(2)+g(2)$.

Since no graphs are given, we cannot provide specific numerical answers. But the steps to solve each part are as shown.