Both Trapezoidal Rule and Simpson's Rule give the same result when applied to any polynomial of degree

Q: What is the area of a quadrilateral with vertices at (-2,-6), (1,-6), (-2,0), and (1,0)? Enter the…

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Q: Given f(x) = 3x+8, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x) h Part: 0 / 2 Part 1 of 2 (a)…

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Q: The following differential equation (+1)² + 2²/ x2 dy x² has an order of 02 3 01 = sin x

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Q: Question The graph of f(x) = -2x³+x-3 is shown below. Use the tools to graph the line tangent to…

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Q: Consider the integral 11 [™ (22² + 2x + 1) da (a) Find the Riemann sum for this integral using right…

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Q: S Use The Fundamental Theorem of Calculus, Part 2 to evaluate X -4 dx.

A: A detailed solution is given below.

Q: ) What function f(t) has Laplace transform: s² +1 f(s) = 5(s² + s−12) 2

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Q: Given f(x) = cos(x) - 2x² + 3x - 1, then f"(0) is equal to- Ο -5 Ο Ο Ο Ο Ο Ο -3 Ο -1 None of them O

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Q: Use the matrices below to perform matrix multiplication. BC= If the operation is undefined, enter…

A: Here we have to do matrix multiplication.

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: 6. Find the radius of convergence and the interval of convergence for E-0¹ (x-2)".

A: 6. The given power series     ∑n=0∞12nx-2n

Q: Test the following series for convergence or divergence. State the test you are using and show all…

A: We need to check whether the given series diverges or converges.

Q: A region bounded by f(x) = 5 — x, y = 0, and x = 1 is shown below. Find the volume of the solid…

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Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: A region bounded by f(y) = √√√y, y = 4, and x = 0 is shown. What is the volume of the solid formed…

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Q: 2. limx-co √x √x+√√x+√x

A: Here we have to find the value of  limx→∞xx+x+x

Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

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Q: a. Use limits to find the derivative function f′ for the function f. b. Evaluate f′(a) for the given…

A: The given function,    fs=5s3+3s, a=-3

Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: What is the area under the graph of y = 2 54-3-2-1 O O N/W 13 2 15 2 ਜਾਨ , -2+ -3 4 1 2 3 4 5 X on…

A: The region is bounded by the graph y=2-x on the interval -2,1

Q: ror(4)). 95. Find the restrictions in the domain, if any, for If there is more than one restriction,…

A: Note: The first question that is question 90 seems incomplete. So, solving 95 for you.

Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

Q: ४ = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: Evaluate the integral using integration by parts. Scot-¹(8y)dy 1 Scot ¹(8y)dy = -x In (cos (6y)) + C

A: The given integral,       ∫cot-18ydy

Q: 2) By using Lagrange multiplier method, find the maximum value of f(x, y, z)=x+ z subject to the…

A: Given function:-     f(x, y, z) = x + z subject to condition x2 + y2 + z2 = 10

Q: Give the domain and range of the graph shown to the right. Then, use the graph to answer parts (a)…

A: Domain :  domain is the  all value of x where the function is defined.

Q: Use the formula for the area of a trapezoid to evaluate √₂² (2x- 2 (2x + 3) dx.

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Q: Determine the volume of the solid under z = 4xy + x² over the rectangle R= [1, 2] × [0, 3]. [Show…

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Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

Q: 15. integral sin 4x cos 4xdx

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Q: Find the derivative of the following function. 8x e y= In 4x y'=

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Q: xp (x+)ɔ zx f

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Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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Q: 1. Evaluate the definite integral *2³²√³+1 dr. (a) ² (27+2√2) (b) (27-2√2) (c)(2√2-27) (d)/(2√2+27)

A: I have stated the used formula in the solution.

Q: A car drives down a road in such a way that its velocity (in m/sec) at time t (in sec) is v(t) =…

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Q: f(x)=2x-7 and g(x) = -18 Given (a) Find (fog)(x). (b) Find (gof)(x). (c) Is the operation of…

A: Given :fx=2x-7gx=1x

Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: B: Draw the function y = √√x-8

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Q: Evaluate x/12 0 14√/1- cos 12x dx.

A: Given, ∫0π4141-cos12xdx

Q: 6. Integral Df ef

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Q: The base of a three-dimensional figure is bound by the line y = x + 4 on the interval [-3, 1].…

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Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A: There are two planes on the XY axis.We are at the origin.  Plane X: The first plane is due west of…

Q: A region bounded by f(x) 6 5 4 3 Find the volume of the solid formed by revolving the region about…

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: To find volume V of the body formed by revolving the given region .

Q: 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2. 2. Find the length of the r(t)= , 1 ≤ t ≤ 5…

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Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: The base of a three-dimensional figure is bound by the line X = √y on the interval [1, 4]. Vertical…

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Q: 12. Integral x² dx x³ +4

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Q: +[ƒ Given that 5 ≤ f(x) ≤ 6 for -4 ≤ x ≤7, use property 8 of Section 5.2 of the Stewart Essential…

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