Certainly! Let's evaluate the function [tex]\( h(x) = e^x \)[/tex] at the indicated values: [tex]\( h(1) \)[/tex], [tex]\( h(\pi) \)[/tex], [tex]\( h(-4) \)[/tex], and [tex]\( h(\sqrt{5}) \)[/tex].
### Step-by-Step Solution
#### 1. Evaluate [tex]\( h(1) \)[/tex]:
We need to find [tex]\( h(1) \)[/tex]:
[tex]\[
h(1) = e^1
\][/tex]
Using the calculator, we get:
[tex]\[
h(1) \approx 2.718281828459045
\][/tex]
#### 2. Evaluate [tex]\( h(\pi) \)[/tex]:
We need to find [tex]\( h(\pi) \)[/tex]:
[tex]\[
h(\pi) = e^\pi
\][/tex]
Using the calculator, we get:
[tex]\[
h(\pi) \approx 23.140692632779267
\][/tex]
#### 3. Evaluate [tex]\( h(-4) \)[/tex]:
We need to find [tex]\( h(-4) \)[/tex]:
[tex]\[
h(-4) = e^{-4}
\][/tex]
Using the calculator, we get:
[tex]\[
h(-4) \approx 0.01831563888873418
\][/tex]
#### 4. Evaluate [tex]\( h(\sqrt{5}) \)[/tex]:
We need to find [tex]\( h(\sqrt{5}) \)[/tex]:
[tex]\[
h(\sqrt{5}) = e^{\sqrt{5}}
\][/tex]
Using the calculator, we get:
[tex]\[
h(\sqrt{5}) \approx 9.356469016601148
\][/tex]
### Summary of Results
[tex]\[
\begin{array}{l}
h(1) \approx 2.718281828459045 \\
h(\pi) \approx 23.140692632779267 \\
h(-4) \approx 0.01831563888873418 \\
h(\sqrt{5}) \approx 9.356469016601148 \\
\end{array}
\][/tex]
These are the evaluated values of the function [tex]\( h(x) = e^x \)[/tex] at the specified points.
