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inna [77]
9 months ago
7

respond to the following in a minimum of 175 of your own words: how would you explain the differences between the trapezoidal ru

le and simpson's rule to a first-year student majoring in math? what do these rules solve? what are the error limits of each method? under what circumstances would you use one method instead of the other?
Mathematics
1 answer:
harkovskaia [24]9 months ago
3 0

The differences between the trapezoidal rule and simpson's rule is -

The trapezoidal rule and Simpson's method, the latter a set of formulas of varying complexity, are both Newton-Cotes formulas, that are used to examine and model complex curves.

<h3>What is trapezoidal rule?</h3>

The trapezoidal rule is just an integration rule that divides a curve into small trapezoids to calculate the area under it. A area under the curve is calculated by adding the areas of all the small trapezoids.

Follow the steps below to use the trapezoidal rule to determine the area under given curve, y = f. (x).

  • Step 1: Write down the total number of sub-intervals, "n," as well as the intervals "a" and "b."
  • Step 2: Use the formula to determine the width of the sub-interval, h (or) x = (b - a)/n.
  • Step 3: Use the obtained values to calculate this same approximate area of a given curve, ba f(x)dx Tn = (x/2) [f(x0) + 2 f(x1) + 2 f(x2) +....+ 2 f(n-1) + f(n)], where xi = a + ix
<h3>What is Simpson's method?</h3>

Simpson's rule is used to approximate the area beneath the graph of the function f to determine the value of the a definite integral (such that, of the form  b∫ₐ f(x) dx.

Simpson's 1/3 rule provides a more precise approximation. Here are the steps for using Simpson's rule to approximate the integral ba f(x) dx.

  • Step 1: Figure out the values of 'a' & 'b' from interval [a, b], as well as the value of 'n,' which represents the number of subintervals.
  • Step 2: Determine the width of every subinterval using the formula h = (b - a)/n.
  • Step 3: Using the interval width 'h,' divide this same interval [a, b] [x₀, x₁], [x₁, x₂], [x₂, x₃], ..., [xn-2, xn-1], [xn-1, xn] into 'n' subintervals.
  • Step 4: In Simpson's rule formula, substitute all of these values and simplify. b∫ₐ f(x) dx ≈ (h/3) [f(x0)+4 f(x1)+2 f(x2)+ ... +2 f(xn-2)+4 f(xn-1)+f(xn)].

Thus, sometimes we cannot solve an integral using any integration technique, and other times we don't have a particular function to integrate. Simpson's rule aids in approximating the significance of the definite integral in such cases.

To know more about the Simpson's method and trapezoidal rule, here

brainly.com/question/16996659

#SPJ4

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Elliot put 7 cups of tea into the pitcher shown. How many more cups of tea does he need to fill the pitcher?
sukhopar [10]

Answer: The Answer would be 9.

Step-by-step explanation:

Since there is only 7 and the empty space is 2 cups, The answer would be 9. 7 + 2 = 9.

8 0
2 years ago
So, Christian has a collection of 18 shark teeth. He identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as
svetoff [14.1K]

Answer:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth. And, the number of bull shark teeth is 4.

Step-by-step explanation:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth.

Since Christian has 18 shark teeth, and 6 are tiger shark teeth, 8 are sand shark teeth and the rest are bull shark teeth.

Let x represent the number of bull shark teeth.

So, total number of shark teeth = number of tiger shark teeth + number of sand shark teeth + number of bull shark teeth.

18 = 6 + 8 + x

18 = 14 + x

subtracting 14 from both sides, we have

18 - 14 = 14 - 14 + x

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4 = x

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So, the number of bull shark teeth is 4.

4 0
3 years ago
Sam needs a web designer. Designer A is offering her services for an initial $500 in addition to $100 per hour. Designer B is of
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2 hours

Step-by-step explanation:

Let's denote the amount of time we need to find out, t.

=> 600 + 50t < 500 + 100t

or 600 - 500 < 100t - 50t

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or 100/50 < t

or t > 2

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The domain of a function is the complete set of possible values of the independent variable. In this case, the independent variable is any nonnegative integer. The nonnegative integers are the set of positive integers along with zero, then,

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3 years ago
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Step-by-step explanation:

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