By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>
In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
- Define the function seen in the statement by the label f(x₀, y₀).
- Determine the different variables by the following formulas:
xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3) - Find the integral.
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
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<h3>
4 Answers: A, C, E, and F</h3>
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Explanation:
Choice A is true assuming we have 
In this case,
and 
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Choice B is false. See choice A above.
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Choice C is true. The sequence
is decreasing. As n gets larger,
gets smaller. This is because the denominator is growing larger with the numerator held constant.
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Choice D is false. This contradicts choice C.
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Choice E is true since the denominator is growing forever
This is similar to 
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Choice F is true due to choices C and E being true.
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Choice G is false because it contradicts choice F.
Answer:
4.1 sec
Step-by-step explanation:
h(t)=-3.2t^2+12.8t+1
h(t)=-3.2(t^2-4t)+1
h(t)=-3.2(t^2-4t+4-4)+1
h(t)=13.8-3.2(t-2)^2
For the ball to touch ground, h(t)=0.
13.8-3.2(t-2)^2=0
(t-2)=2.0766
t=4.07≈4.1 sec.
Start at 15 and move the same direction as the sign <
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Answer: 2 5/8 miles
Step-by-step explanation:
Because 6 1/8 - 3 1/2 = 2 5/8, Alice and Enrique will have 2 5/8 miles left to jog after their break.
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