Use a calculator to evaluate the function at the indicated values.

[tex]\[ h(x) = e^x \][/tex]

[tex]\[ h(1) = \][/tex]
[tex]\[ h(\pi) = \][/tex]
[tex]\[ h(-4) = \][/tex]
[tex]\[ h(\sqrt{5}) = \][/tex]



Answer :

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.