2.Evaluate the following integral: fx²cosxdx (a) by solving the integral analytically; by solving the integral numerically using (b) multiple-application trapezoidal rule, with n = 6; (c) multiple-application Simpson's 1/3 rule, with n = 6;

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A: Given,         3, 4, 4, 5, 6, 6, 7, 8, 8, 9

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A: Solution:-

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A: The von Bertalanffy equation is defined by ODE as follows W'(T) = αW(t)2-βW(t)Let  y(t) = W1-λdWdt =…

Q: Q5: Consider the following subsets of real plane R²¹ Determine with graph: 1-Arewise connected A=…

A: Here we have a common point in both of the sets. Also thos two sets are individually connected.

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Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy…

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A: If f is continuous and non negative on the interval α≤θ≤β with 0<β−α≤2π. Then area of the region…

Q: 4. y" - 4y + 5y = g(x); y(0) = 1, y'(0) = 0 where g(x) = x if 0 < x < 1, and g(x) = 0 if x ≥ 1

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Q: Q5: Consider the following subsets of real plane R² Determine with graph: 1-Arewise connected A=…

A: Follow the steps.

Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

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Q: 31. Ke [<cos (1₂) c² - 3+₁ ²+/=/=) +‡ -1 (-1,19,-27, t = 11. Ŕ(t) (1) show that I is continuous at t…

A: This is a problem of vector calculus.

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A: we will find equations of traces and then find type of surface represented by comparing with…

Q: Given: polar curves C₁ : r = √2- cos 0 and C₂ : r = √2+ sin intersecting at A(³√2, 37) and B(2,7) 2…

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A: Let us start solving the problem step by step... Given x2+y2-2y=0 y=2-x Revolving about y=0

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A: Solution

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Q: 7. Find the equation of the circle with center (2, -4) and tangent to the y- axis.

A: As per guidelines we are supposed to solve the maximum one questions at a time. plz repost another…

Q: Solve the nonhomogeneous system ty' = 3-2 2 -2 Y + -2t ¹-1

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A: We can solve using given information

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Q: and m' be two R-modules. e set Hom, CM, Mm) is an group under pointwise of morphism

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Solution :-

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Q: b) Solve: P(4)=4-5t + tetsint

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Q: *Problem 3.2 Consider the collection of all polynomials (with complex coefficients) of degree < N in…

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Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

A: Follow the steps.

Q: 5. D = 2000 2 1 -5 Evaluate D.

A: 2  0  0   0-5  3  0   0   3  2  4   0   4  2  1-5  =  (2)(-1)1+1 3  0   02  4   02  1-5…

Q: b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy…

A: Variation parameter method

Q: The curve defined by R(g) = 1. Considering f(g) to be a function such that f (1) = 0 and f' (1) =3.…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Q3: Use finite difference method to solve Laplace equation in the red (hand written plzzz) domain…

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Q: 2. Find the inverse of A = 1 1 1 1 2 -1 3 1 -1 2 3 H2H2 1 using Gauss-Jordan method.

A: The solution is given as

Q: - (² homogeneous system ty' = 2 -2 Y +

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Q: (c) Find the slope of the objective function. Slope = (d) What are the values of x and y that give…

A: given objective function fx,y=30x+42y (c) slope of the objective function it is known that function…

Q: Find the solution of the following Differential Equation using Inverse Leplace: ý = 4y+3y=0 ẤY >…

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Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

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Q: B = 0 -2 12 4 −1 -1 3 4

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…