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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<span>tan(15) =
sin(15) / cos(15) =
sin(45 - 30) / cos(45 - 30) =
[ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)]
Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom
[ cos(30) - sin(30) ] / [ cos(30) + sin(30)]
[ √3/2 - 1/2 ] / [ √3/2 + 1/2]
(√3 - 1) / (√3 + 1)
(√3 - 1)^2 / (√3+1)(√3 - 1)
(√3 - 1)^2 / (3 - 1)
(3 - 2√3 +1) / 2
2 - √3
There's also a formula for tan(a-b), but I couldn't remember it off hand.</span>
Answer:
7/10
Step-by-step explanation:
this is the simplest form
Well you are given the roots.
if we have 3 it would.have to be x^3. So something like:
y = ax^3 + bx^2 + cx + d
this could.also be written:
y = (x + a) (x + b) (x + c)
when you are able to write it like this, we know that the opposite of a, b, and c are roots. this is because if we can make any of the insides of the 3 parenthesis equal 0 then y = 0 and that x.is a root. Well if we know the 3 roots that x will be then we just have to figure out the a, b, and c. So let's plug our roots in.
y = (-1 + a) (-5 + b) (-3 + c)
now we have to make each parenthesis equal 0 to find what a, b, and c should be. It is obvious a = 1 to make.that one zero and b = 5 and c = 3. So we know a, b, and c. now let's plug.those into our first equation.
y = (x + 1) (x + 5) (x + 3)
this is your equation. You can multiply out if necessary
