Consider the error formulas. IEl s 6 - a), -[max If"(x)|], asxsb Trapezoidal Rule 12n2 (b – a)5 180n4 JE| S [max |f(4)(x)|], asxsb Simpson's Rule Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule. %3D '3 'a? + 74) dx (a) Trapezoidal Rule (b) Simpson's Rule

Q: 3. If y x- 15x', find; x– 15x², find: a) Intervals of increase/decrease.

A: We’ll answer the 3rd question since we answer only one question at a time. Please submit a new…

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Q: Find an equation for the line tangent to the graph of 2x f(x) %3D x + 4 at the point (2,…

A: The standard form of the tangent helps to find the required equation. The standard form of the…

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A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

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A: Given: 1) f(x)=2x3-5x2+8 and the interval 1, 5. To find: a) The area under the curve over the…

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Q: Problem 4: Find the inverse of the following matrices, using the Gauss-Jordan method. [1 C = 3 12 2…

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Q: Differentiate the function. H'(z) = H(z) = In c²-2² c²+z²

A: H(z)=lnc2-z2c2+z2

Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: If f(4) 8 and f '(x) 2 1 for 4 < x < 9, how small can f(9) possibly be?

A: Given:- If f(4) = 8 and f '(x) &gt; 1 for 4 ≤ x ≤ 9 To find:- How small can f(9) possibly be?

Q: Consider the function below. x2 f(x) : x2 - 25

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Q: Use a plot of f(x) = x* to estimate the value c such that f'(c) = 0. Find c to sufficient accuracy…

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Q: Let y = || = y'"' = = x + 7 X X Hint: Try to do this without using the quotient rule.

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Q: 16. r(0) = sec 0 tan 0 – 2eº -

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Q: (2.00-x) Vq₂ = ±xV|q₁|

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Q: Entered Answer Preview 42 - 3°(In(3) +1) 64255.3 2x Let f(x) = 4x2". Find f'(3). %3| f'(3) =…

A: This question is based on Derivative of function.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.