Using principle of mathematical induction, prove that 3. 1° + 2° + 3° +.... +n = n(n + 1) 2

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A: We want to find Taylor series of f(x) = cos(x) at a = π2

Q: Sther question will save this response. Question 2 Use Laplace transforms to solve the differential…

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Q: Using principle of mathematical induction, prove that 3 + n n(n + 1) 2 1° + 2° + 3° + •....

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Q: If the cardinality of a set A is 4 and that of a set B is 3, then what is the cardinality of the set…

A: Given the cardinality of a set A is 4 and that of set B is 3 . Then to find the cardinality of set…

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Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

Q: Question 3 Find the Laplace Transform of e 2t cos3t + 5e 2t sin3t 15 + A s2+9 s2+9 s+17 B (s+2)²+9…

A: laplace transform

Q: Which of the following is the general solution to the differential equation + 2x - 2x*y'dy dx+ 2x

A: We have to find the general solution to the given differential equation.

Q: The inverse of the matrix shown below is: [5 31 L10 6] В. [5 31 L1.0 .6] C. [.167 .11 [.33 2] А. D.…

A: We know the inverse of matrix A =  abcd is given by,A-1 = 1ad-bcd-b-ca     where, ad-bc ≠0

Q: 2. f(t) = e-5tcosh(6t) – (9t)7/2

A: We will use the given table for Laplace transformation to get our required result.

Q: Question 4 MO21. A civil engineer is analyzing the compressive strength of concrete. Compressive…

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Q: Suppose that f is continuous on [0, 1], ƒ(0) = 0, and f'(0) exists. Prove that the Lebesgue integral…

A: This is a question of measure theory.

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Q: which is the collection of all polynomials of degree ≤ 3. Write out the standard basis for P2? What…

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Q: What is the Laplace transform of f(t) = te? A. s+ es B. 1/(s+1)? C. 1/(s-1)? D. s2 + es

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Q: Question 2 In this question we are considering the vector space P2, which is the collection of all…

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Q: 3. Use your ruler to draw your own triangle and vector . Explain how to use your ruler to translate…

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Q: If F(p) and G (p) are the Mellin transforms of the functions f(x)

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Q: Consider the following IVP: x" - 4x' + 4x = 4e; x(0) = -1, x'(0) = -4 Find the general solution. A…

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Q: Find the area bounded by the curves f(x)=x+8 and g(x)=x²-x.

A: The area between the curves fx and gx on the interval a,b is given by ∫fx-gxdx. Setting fx and gx,…

Q: Find the Laplace Transform of e4t + 5 + - S-4 B 1 + - .4 1 s+4 1 + S+4

A: We have to find the Laplace transform.

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Q: IF F= 3yI - Xy I+ 9ZK and s is the Surface of the Pasabolied 2X =x2 fy Bounded By Evaluate %3D I=2…

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Q: ponse. Question 2 Use Laplace transforms to solve the differential equation y'(t) +5y(t) = 10H(t-…

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Q: (x+6)-(5-2x)+2=0

A: Given equation: (x+6)-(5-2x)+2=0

Q: Find the Laplace transform of g(t) = 4cos(4t) - 9sin(42) + 2cos(10t) 9 A G(s) = s?+4 s²+16 s?+ 100…

A: To find Laplace transformation of  g(t) = 4cos(4t) - 9 sin(4t)+ 2cos(10t)

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A: Given : 3-regular connected planar graph

Q: Let f(n) = n and g(n) = log2 n. Show that g e O(f) but f ¢ O(g).

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Q: dy What is the general solution to the differential equation -y = (2) sin x ? %3D dx y = x?(2x cos x…

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 -21…

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Q: Theorem 3.1. Let V be an inner-product space and vectors x, y e V, then |(x, y)|< || x || | - Strict…

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Q: Which of the following is the general solution to the differential equation dx + 2x = 2x²y²dy ? %3D…

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Q: The addition of matrices shown below gives: Гз 7 27 10 0 and [5 3 4] Г2 47 Li 3] А. Зх3 matrix B. 3…

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Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: Which of the following is the general solution to the differential equation dx – 2xydy =…

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Q: Find the area to the left ofz = -1.96 or to the right of z = 1.96?

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Q: Given that z is a standard normal random variable, what is the value of the z score (a) if P(z2a)…

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Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

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Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) =…

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Q: 2s + 3 Find the Inverse Laplace Transform of F (8) s2+ 4s + 13 A f(1) = e2 2sin3t – -cos3t B f(1) =…

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Q: 3. Use the definition to prove that limr→∞ x² 00.

A: Given : The given function is ;  f(x) = x2 To prove :  By the use of definition, we have to prove…

Q: Use integration by part to obtain a formula for S x"e®*dx and use it to find S x°e*dx. n Bx 3 5x

A: We have to find the formula for given integral.

Q: cos(s")dtds

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 -'cos3t B -Isin9t 3 cost 9 -'sin3t (D 3

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Q: If M and N be the subspaces of V that contains the set of symmetric and skew- symmetric matrices,…

A: Given M be the subspace of symmetric matrices and N be the subspace of skew- symmetric matrices