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: MARQUEZ, YSLE RHE INE BSME IB COE 102 Given: y xC xt3)? ở. ye x[2Cx13)C1)]+ (x13)°C1) y: 2x Cx+3) +…

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Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

A:

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…

Q: In which interval, function f(x)=x3e-x is increasing and concave up? (0, 3(sqrt3)) (3-sqrt3, 3) (3,…

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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…

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

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

Q: One method to obtain an approximate solution is to plot the function and determine where it crosses…

A: True  is correct ans

Q: Let f(x)=V2x/x. Then f"(1)= Select one: 3 16 3 8/2 - 36 7 21 O None of the above

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Q: 1) Consider the function f(x) = 2x³- 5x² +8 over the interval [1,5]. a) Approximate the area under…

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

Q: Evaluate V7 by using linear approximation of f(x) = V about the value I = 8.

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Q: If ƒ(x) = (6x² − 2) (4x + 6), find: f'(x) = Suggestion: Verify using product rule and by simplifying…

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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: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

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: Find the exact extreme values of the function : = f (r, y) = 49r + 13y + 50 subject to the following…

A: The region provided by the constraints 0≤y≤9-x2 is obtained as follows:

Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: consider the ff. function: f(x, y) = cot" "^ (1+x) - 2x + ³y 3y 2e

A: Given the function             f(x, y)=cot-1(1+x)-2ex+3y Where              x=s2+t2,  and…

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.

Q: Hiwiy Express the ballowsing functions by Palar equationft 2.

A: To change a rectangular equation to a polar equation just replace x with (r cos θ ) and y with  (r…

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.