3) Find the expention of sin³ 0 4) Proof that: cosh iz = cos z 5) Prove that: cosh² z - sinh²z = 1 6) Prove that: cosh² z + sinh²z = cosh 2z

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A: We have to prove that a norm · is induced by an inner product if and only if, for all x,y∈V , the…

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A:

Q: Use flat random numbers to estimate л.

A: Let us estimate the pi using flat random numbers in the next steps.

Q: 8. Solve the recurrence relation an = given do = 40, a₁ = = 37. 2an-1-an-2, n ≥ 2,

A: Given recurrence relation is an = 2an-1 - an-2 , n ≥ 2 given a0 = 40, a1 = 37

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A: The solution starts with the next step.

Q: Exercise II Use the method Laplace transform to solve the following. (a) = 1₂-1₁ +1₁ 2²₂2 = 1₂.

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A: We have to solve the differential equations.

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A:

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A: Given,f(x)=3x-x2-ex-2+5xl=-2 , xu=4 , ξs=0.000005To find: Maximum value of f(x) using Golden-Section…

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Q: /xy2. +xzu+yv2-3 = 0 The system of equations: |6x3y2 + 2xv - 3u²v2 - 5 = 0 - can be solved for y and…

A: Given system of equations xy2+xzu+yv2-3=06x3yz+2xv-3u2v2-5=0          .......(1) where x,u and v are…

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A: We have to find the characteristic polynomial.

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Q: form of (3+3i)^5

A: Given,      (3+3i)5

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A: The given function is f:a,b,c,d,e→1,2,3,4 with fa=3, fb=1, fc=2, fd=4 and fe=2.  To find : (a) The…

Q: Referring to the figure, suppose that fo F. dr = 2n fo F. dr = 5n - Use Green's Theorem to determine…

A: Given- Referring to the given figure, suppose that ∮C2F·dr = 2π∮C3F·dr = 5π To find- Use Green's…

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A: Centre of mass of bounded by the curves in first quardent

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A: Rewrite the given differential equation. y'=x24-y2             ...1

Q: 1. Consider the differential equation z³y(3)-3ry' +6y=0. (a) Find distinct values of r, say 71,…

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A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

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A: The solution is below.

Q: Evaluate the following integrals. 4x+10 1. S dx (x-2)(x-1)²

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x=3.

A: Given y = 5x4

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Q: Evaluate curl of A and divergence of curl of A, if A = x²yax + y²zay - 2xzaz

A:

Q: Find the average value of f(x,y) = x² + y² over the region R: rectangle with vertices (0,0), (2,2)…

A: Introduction:   A function f(x,y) average value as defined by favg=1A(R)∬Rf(x,y)dA   where A(R)…

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A: Given: Four hour growth rate is 54%. To determine: One hour growth rate.

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

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A: Solution

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A: We want to find true option.

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Q: Example 7.16. Given the table 310 320 330 log x : 2.49136 2.50515 2.51851 find the value of log…

A: Let us find the value of log(337.5) by Everett's formula in the next steps.

Q: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

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A: Please type correctly

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A:

Q: Consider the differential equation y'' - 2xy' + y = 0 subject to y(0) = 1 and y'(0) = 5. The first…

A: To solve this problem just we need to put the value of x in given y(x)  and then use the following…

Q: (cos 3x - x²) (sin 3x-x³)5 dx cos² x (tan x) (sec² x - 1) dx

A: 1st question solved by substitution rule and 2nd question solved by identities rule.

Q: Which of the following are valid witnesses to show that 10n-1 is (n)? O C=1, k=100 O C=10, k=10 O…

A: