Answer :
Certainly! Let's evaluate the function [tex]\( h(x) = e^x \)[/tex] at the indicated values [tex]\( x = 1, \pi, -4, \sqrt{5} \)[/tex] and round our answers to three decimal places.
1. Evaluating [tex]\( h(1) \)[/tex]:
- The function [tex]\( h(x) = e^x \)[/tex] means we need to calculate [tex]\( e^1 \)[/tex].
- [tex]\( e^1 = 2.718 \)[/tex] (rounded to three decimal places).
2. Evaluating [tex]\( h(\pi) \)[/tex]:
- Here, we need to evaluate [tex]\( e^\pi \)[/tex], where [tex]\(\pi \approx 3.141592653589793\)[/tex].
- [tex]\( e^\pi \approx 23.141 \)[/tex] (rounded to three decimal places).
3. Evaluating [tex]\( h(-4) \)[/tex]:
- We need to find [tex]\( e^{-4} \)[/tex].
- [tex]\( e^{-4} \approx 0.018 \)[/tex] (rounded to three decimal places).
4. Evaluating [tex]\( h(\sqrt{5}) \)[/tex]:
- Lastly, we need to calculate [tex]\( e^{\sqrt{5}} \)[/tex], where [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex].
- [tex]\( e^{\sqrt{5}} \approx 9.356 \)[/tex] (rounded to three decimal places).
So, our evaluated and rounded values of the function [tex]\( h(x) = e^x \)[/tex] at the specified points are:
- [tex]\( h(1) = 2.718 \)[/tex]
- [tex]\( h(\pi) = 23.141 \)[/tex]
- [tex]\( h(-4) = 0.018 \)[/tex]
- [tex]\( h(\sqrt{5}) = 9.356 \)[/tex]
These are the final results.
1. Evaluating [tex]\( h(1) \)[/tex]:
- The function [tex]\( h(x) = e^x \)[/tex] means we need to calculate [tex]\( e^1 \)[/tex].
- [tex]\( e^1 = 2.718 \)[/tex] (rounded to three decimal places).
2. Evaluating [tex]\( h(\pi) \)[/tex]:
- Here, we need to evaluate [tex]\( e^\pi \)[/tex], where [tex]\(\pi \approx 3.141592653589793\)[/tex].
- [tex]\( e^\pi \approx 23.141 \)[/tex] (rounded to three decimal places).
3. Evaluating [tex]\( h(-4) \)[/tex]:
- We need to find [tex]\( e^{-4} \)[/tex].
- [tex]\( e^{-4} \approx 0.018 \)[/tex] (rounded to three decimal places).
4. Evaluating [tex]\( h(\sqrt{5}) \)[/tex]:
- Lastly, we need to calculate [tex]\( e^{\sqrt{5}} \)[/tex], where [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex].
- [tex]\( e^{\sqrt{5}} \approx 9.356 \)[/tex] (rounded to three decimal places).
So, our evaluated and rounded values of the function [tex]\( h(x) = e^x \)[/tex] at the specified points are:
- [tex]\( h(1) = 2.718 \)[/tex]
- [tex]\( h(\pi) = 23.141 \)[/tex]
- [tex]\( h(-4) = 0.018 \)[/tex]
- [tex]\( h(\sqrt{5}) = 9.356 \)[/tex]
These are the final results.
