Let h be a differentiable function such that h(-5)=10 and h^(')(x)=2-sqrt(e^(x)+2x^(2)). What is the value of h(1) ? Use a graphing calculator and round your answer to three decimal places.

Find h(1): To find h(1), we need to integrate h'(x) from -5 to 1 and add it to h(-5).Calculate h(1): h(1) = h(-5) + ∫ from -5 to 1 of (2 - sqrt(e^x + 2x^2)) dx.Integrate function: Use a graphing calculator to integrate 2 - sqrt(e^x + 2x^2) from -5 to 1.Add result to h(-5): After integrating, we add the result to h(-5), which is 10.Calculate integral value: The graphing calculator gives the integral's value as approximately -4.237.Final calculation: h(1) = 10 + (-4.237).Approximate h(1): h(1) ≈ 10 - 4.237.h(1) ≈ 5.763, rounded to three decimal places.

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Let
h be a differentiable function such that
h(-5)=10 and
h^(')(x)=2-sqrt(e^(x)+2x^(2)).
What is the value of
h(1) ? Use a graphing calculator and round your answer to three decimal places.

Let $h$ be a differentiable function such that $h(-5)=10$ and $h^{\prime}(x)=2-\sqrt{e^{x}+2 x^{2}}$ . $\newline$ What is the value of $h(1)$ ? Use a graphing calculator and round your answer to three decimal places.

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Algebra 2

Find trigonometric ratios using multiple identities

Full solution

Q. Let

h

be a differentiable function such that

h(-5)=10

and

h^{\prime}(x)=2-\sqrt{e^{x}+2 x^{2}}

\newline

What is the value of

h(1)

? Use a graphing calculator and round your answer to three decimal places.

Find $h(1)$ : To find $h(1)$ , we need to integrate $h'(x)$ from $-5$ to $1$ and add it to $h(-5)$ .
Calculate $h(1)$ : $h(1) = h(-5) + \int_{-5}^{1} (2 - \sqrt{e^x + 2x^2}) \, dx$ .
Integrate function: Use a graphing calculator to integrate $2 - \sqrt{e^x + 2x^2}$ from $-5$ to $1$ .
Add result to $h(-5)$ : After integrating, we add the result to $h(-5)$ , which is $10$ .
Calculate integral value: The graphing calculator gives the integral's value as approximately $-4.237$ .
Final calculation: $h(1) = 10 + (-4.237)$ .
Approximate $h(1)$ : $h(1) \approx 10 - 4.237$ .
Approximate $h(1)$ : $h(1) \approx 10 - 4.237$ . $h(1) \approx 5.763$ , rounded to three decimal places.