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trasher [3.6K]
3 years ago
15

Find the area of the region under y=e^x and above y=1 for 0 less than equal to x less than equal to 5.

Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0
\int\limits_{0}^{5}(e^x-1)dx=\int\limits_{0}^{5}e^xdx-\int\limits_{0}^{5}1dx=e^x|^5_0-x|_0^5=e^5-e^0-(5-0)=
\\
\\=e^5-1-5=e^5-6
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Answer:  see below

<u>Step-by-step explanation:</u>

Domain represents the x-values from the smallest (furthest left) to the biggest (furthest right).

Range represents the y-values from the lowest (furthest down) to the highest (furthest up).

Interval notation: If a value is included <em>(closed dot)</em>, use a bracket [  ]

                      If a value is NOT included <em>(open dot)</em>, use a parenthesis (  )

                     Note that ± ∞ is never included.

1. Domain: smallest x-value is -4 (included). biggest x-value is 3 (included)

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2. Domain: smallest x-value is -∞ (←). biggest x-value is 2 (included)

  Range: lowest y-value is 2 (included). highest y-value is ∞ (↑)

                 D: x = (-∞, 2]        R: y = [2, ∞)

3. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

  Range: lowest y-value is -∞ (↓). highest y-value is ∞ (↑)

                 D: x = (-∞, ∞)        R: y = (-∞, ∞)

4. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

  Range: lowest y-value is -∞ (↓). highest y-value is 4 (included)

                 D: x = (-∞, ∞)        R: y = (-∞, 4]

5. Domain: smallest x-value is -∞ (←). biggest x-value is ∞ (→)

  Range: lowest y-value is 3 (included). highest y-value is ∞ (↑)

                 D: x = (-∞, ∞)        R: y = [3, ∞)

6. Domain: smallest x-value is -2 (included). biggest x-value is ∞ (→)

  Range: lowest y-value is -3 (included). highest y-value is ∞ (↑)

                 D: x = [-2, ∞)        R: y = [-3, ∞)

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Answer:

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Step-by-step explanation:

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