Math Problem Statement

Use a calculator to evaluate the function at the indicated values. Round your answers to three decimal places. h(x) = ex; h(1), h(𝜋), h(−2), h(

h(

5 )

Solution

The values of the function h(x)=exh(x) = e^x at the indicated points are:

  • h(1)=2.718h(1) = 2.718
  • h(π)=23.141h(\pi) = 23.141
  • h(2)=0.135h(-2) = 0.135
  • h(5)=148.413h(5) = 148.413

Do you want more details or have any questions?

Here are some related questions to explore:

  1. What is the behavior of exe^x as xx approaches infinity?
  2. How does the function exe^x change when xx is negative?
  3. What is the derivative of h(x)=exh(x) = e^x, and how can it be interpreted?
  4. Can you explain the significance of the value ee?
  5. How does h(x)=exh(x) = e^x compare with other exponential functions like 2x2^x?

Tip: The exponential function exe^x grows rapidly for positive xx, and decays towards zero for negative xx.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Euler's Number (e)
Function Evaluation

Formulas

h(x) = e^x
Approximate value of Euler's number e ≈ 2.718

Theorems

Exponential Growth
Properties of the Exponential Function

Suitable Grade Level

Grades 10-12