Compute the definite integral T/4 0 5 sin² (3x) dx

Q: a. Find Taylor Expansion of the following Functions about xo =0 b. Find Taylor Expansion of the…

A: Sol:- Taylor expansion about x0 = 0 Taylor series of function fx at a is defined…

Q: 9. 10. Neville's Algorithm is used to approximate ƒ(0) using ƒ(−2), ƒ(−1), ƒ(1), and ƒ(2). Suppose…

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Q: c. A certain radioactive material is known to decay at a rate pr amount present. If after one hour…

A: Lets say amount of the radioactive material present at time 't' be 'N'.

Q: How many rows of A contain a pivot position? Does the equation Ax = b have a solution for each b in…

A: Given matrix is A=24−90−2−2440−615−12201−9. First of all reduce the given matrix A into echelon form…

Q: 5) L (4 4 sinh 3 2t +3 sinh 2tỷ

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Q: Find solution of the equation x2 = 17 by the Newton's method.

A: We find the solution of x2=17 by Newton's method.

Q: Given d'y dx² = 6x-0.5x², y(0) = 0, y(12)=0, Use step size h = 4, z1 = 20, and z2 = 25. Enter 4…

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Q: y=x² + 2x + 1 and y= 8x +8 1.) The appropriate integrand to find the area of the plane region it! 2…

A: Area between two curves y=f(x) and y=g(x) where f(x)≥g(x) from [a, b] is  A=∫ab(f(x)-g(x))dx

Q: c. A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Sol

Q: For the initial-value problem: y = y-t²+1, 0≤ t ≤ 2, y(0) = 0.5, h = 0. 1, N is equal to --- 20 O 5…

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Q: 2. Use root test to determine whether the following series is convergent or divergent: 00 Σ n=2…

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Q: 2. Use ratio test to determine whether the following series is convergent or divergent: (2n)! Σ n.…

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Q: c. A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: let amount of material present at any time t be p(t) let p0 be the intial  amount of material at…

Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: System of linear equations is Inconsistent if System has no solution System has unique solution O…

A: The solution is given as

Q: Solve parts a) and b). a) Find all polar coordinate representations (r.0) where 0ses 2n of the…

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Q: Question 3 In the figure given below, there is a horizontal channel PS which is fixed. And two rods…

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Q: Solve for the 1.Fixed Point-Alteration 2.Newton-Raphson Method 3.Secant Method a. 4x² + 3x - 3=0

A: According to guidelines we can solve only one problem

Q: 14- If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is (a) 0.5833…

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Q: 7. Let V be a 70-dimensional vector space and let W₁ and W2 be 30-dimensional subspaces. What is the…

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Q: For the following initial-value problem: ý = y-t²+1, 0≤t≤ 2, y(0) = 0.5, h = 0.125,----- is the…

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Q: Q3.B. Find a general solution of the following differential equation using Laplace transform. y" -…

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Q: By using Simpson's 3/8 Rule alone, one can approximate the area under a curve when the number of…

A: This question related to numerical integration.

Q: To approximate y(2.75) for the following initial-value problem: ý = y + t²,1 ≤t≤ 3, y(1) = 2, the…

A: We need to approximate y2.75 Now, 1≤t≤3 Now, xn=x0+hn If we choose h=0.15 then:…

Q: Solve for за + ад ду-4 = 2- 24 Z 2 2 а 20-2

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Q: 8. Consider linear spline function L(x): Let f(x) = ln(x + 2), Given (0, 2), (-1, 4) and (1, 6).…

A: Sol

Q: Evaluate the following integral: La-e²³) dx d. Composite trapezoidal rule, n=4 e. Simpson's 1/3 Rule…

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Q: Q1.A. Determine the inverse Z-Transforms of the following function: z² (2z + 1)(z-1) F(z)

A: Given: Fz=z22z+1z-1 To determine the inverse z-transform of the following function.

Q: 6. Approximate the solution to the following set of equations using iterative procedure and using…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: of am regulay space X and it subset of X such that cey them there is subset o a closed neighbourhood…

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Q: Incorrect. If y, and y₂ are linearly independent solutions of t²y" + 2y + (5 + t)y = 0 and if W(y₁,…

A: We solve by using Abel's Formula.

Q: Find the Fourier Series expansion of the function f(t) = t & f(t) = -2m(-1)" b. O a Ob O c Od c.…

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Q: 7. The absolute norm for tensor of two eigenvectors of A = (23) is (b) √3 (c) 1/3 (a) 3 (d) None of…

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Q: Solve for

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Q: Construct a graph with vertices I, J, K, L, M, N that has an Euler circuit and the degree of L is 4.…

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Q: Consider the real inner product space P[0, 1] of all polynomials with the inner product, (f,g) =…

A: This question related to orthogonal projection from linear algebra.

Q: Q3./ Solve the following simultaneous ODE y₁ = -3y₁+ Y₂ −3 y₂ = Y₁ - 3 Y₂

A: To solve the  given problem, we use the standard defination of differential  equations

Q: (³x-2x4) p + (2y4-x³y) a = 92 (x³ - y3)

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Q: Suppose p. q. and r are simple statements. Use grouping symbols to write the following logical…

A: given logical statement p∧r⇔q⇒p∨r

Q: Plot the following and their normal vectors. 2x-2y + 2z = 15 3x - 3y + 3z = -13 Describe the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: System of linear equations is Inconsistent if System has no solution O System has unique solution O…

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Q: 4) L'{ + } હ ર (+)4

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Q: QUESTION 1 A study was made on the amount of converted sugar in a certain process at various…

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Q: Calculate square root of 19 by the secant method.

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Q: y=-3 y₁+ y₂ y₂ = y₁ - 3 y₂

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Q: e. To solve the 2nd order ODE, xy" - (x + 1) y' - y = 0, by series method, the indicial roots are…

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Q: 1. tan² (x)+x²e¹-2 dx 2. Order Linear / Nonlinear (circle the correct answer, +cos(2x+3)x¹+2x² dx…

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Q: 3. Let W be the subspace of R3 [x] spanned by the polynomials 1+2x+3x²+4x³, 2+3x+4x²+x³, 3+4x + x² +…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Using the function f(x) = sin x over the interval [0, 1], find an upper sum; let n = 6.

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