Find the least value of n so that T, (Trapezoid rule with n subintervals) is guaranteed to approximate cos(3 x) dx to within 0.04. a) On= 24 p) On= 23 =) On = 11 3) On= 27

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Q: Q2: In usual topological space (R.T), answer the following: 4- Is [0,1] is arcwise in R? Why?

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Q: . Use the inegral test to show that =1 1+n2 100 converges. hDoes the alternating serios tost anply…

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Q: The approximation of I defined in exercise 5 using Composite Simpson's rule with n= 4 subintervals…

A: Given I = ∫12dx5-x2 Let f(x) = 15-x2 We need to divide it in 4 intervals , hence the width of each…

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Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: Let be the boundary surface of the box enclosed by the planes x = 0,  x = 2, y=0, y = 4, z =0 and z=…

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Q: Let D be the solid region in space bounded below by p = and above by cosp p = ". Then the region D…

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Q: Find the domain and limit ast approaches infinity of T(t): i+ [2e ]j+[arctan(t)] k 3 In %3D 7.

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Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

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Q: For the region under f(x) 5x on [0, 2], show that the sum of the areas of the upper approximating…

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Q: Let D be the solid region in space bounded below by p = -- and above by cosp p = . Then the region D…

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Q: 3. Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- gin, and f(z) = 1+…

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Q: 1 Let D be the solid region in space bounded below by p =- and above by cosp p = Then the region D…

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Q: This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals…

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

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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.