If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

Q: 1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + f (x + ct)) + f + g(s)ds by determining the…

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Q: E.S. nsider the following matrix: 1 1 0\ A=0 2 0 0 3 0 ➡blem E.3.a. Find the eigenvalue(s) and the…

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Q: Determine the area enclosed by each polygon. Use the natural unit. (a) (b) units

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 7. Express 55C14 + 54C14 +54C15 as a single term from Pascal's triangle.

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Q: Find an area similar to the example f(x)=x^2 from [0,1] that we couldn't have computed from…

A: Given That: f(x)=x2 To Find : Area using Riemann sums

Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line…

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Q: Given that find the Laplace transform of √cos (8t) C{√/cos(8t)} = (-16)^(-8/s)/(88 (5/8)) CL cos(8t)…

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Q: Brendan needs $12 000 in 3 years for college. How much must he invest today at 8.9%, compounded

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Q: III. Given the focus and directrix of the graph of a parabola identify its important…

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Q: 77541 Solve the following LPP by Dual Simplex method. Min +255x1 +681 s.t. x1 + x2 ≥ 2 4x1 + x2 ≥ 4…

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Q: а) Рrоⅴе thаt І = { f(х) ∈ ℤ[х] : f(0) іѕ еⅴеո } іѕ аո іⅾеаⅼ оf ℤ[х].

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Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

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Q: Miss Basson is taking her Gr 10 class on an outing to the Zoo. She has a class of 35 learners of…

A: It is provided that there are 35 learners in total and 92% can join the outing. The pay for each…

Q: (a) Determine the validity of the following argument using Venn dia Everyone who is sane (of sound…

A: 1(a) determine the validity of the following argument using venn diagram everyone who is sane can do…

Q: Consider the initial value problem: ty" - 2t2y" + 3ty' - 3y = t², y(1) = 1, y' (1) = 0, y" (1) = 1…

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Q: 8. The vector field F(x, y, z) = (2xz + y²)i + 2xyj + (x² + 3z²)k is conservative. Find a potential…

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Q: VII. Suppose is the surface generated by revolving the curve y = 4(²-1) about the y-axis. 1.…

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

Q: Determine whether the given matrix A is diagonalizable. If so, find the matrix P that diagonalizes A…

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Q: Find all values of the full power. ASAP 2 (ei)√₂

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Q: 3y > » √+x4 Definc f(x,y) (a) Find the rate of change of f at the point (-1,1) along the direction…

A: Given: fx,y=3y1+x4 To find: (a) Rate of change of f at the point (-1, 1) along the direction <1,…

Q: PROBLEM 7: Solve the following differential equation from t = 0 to 1 dy dt with the initial…

A: 7a). Hint: Use the separation of variable method and solve the given differential equation with the…

Q: Find and sketch the domain of flx,y) =√√₁-(x + ₁)² - y² + 2 in (x-y +1). 1-

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Q: Discuss the analyticity of  f(z) = Re(z 3)   Find whether the given function is analytic or not.…

A: A complex valued complex variable function is analytics at z0 if it is differentiable every point in…

Q: In the diagram below ZA = 38°. Side a measures 12 cm. What is the measure of ZB? Express your answer…

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Q: 4. Solve the Cauchy problem Utt = 9uxx+cos x, (x, t) E Rx (0, ∞) u(x,0)=0, TER u(a,0)=0, x ER using…

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Q: onsider the smooth parametric curve C defined by the equations Jx = t t (t²-3) Y = 3 (t² − 3)' here…

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Q: Solve the following initial-boundary-value problem by using the separation of variables technique:…

A: Given :             utt=uxx                0≤x≤1   ,   t>0 u0 ,t =0  ,u1 ,t =0…

Q: Problem E.1. Consider the following matrix: A = (²₁³) Problem E.1.a. Find the eigenvalue(s) and the…

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Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

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Q: Find a first-order L²-approximation for the following equations f(x) = sin x f(x) = e-3x 0≤x≤1…

A: We have to solve given Questions.

Q: 2 Find the surface area of the portion of the cone x² + y² = 2² above the region inside the…

A: we have to find the surface area of the portion of the cone x2+y2=z2 above the region inside the…

Q: 3t 1+f3.y te Consider the parametric equations x = 3t² ‡ 1+ 3,¹ -1. Its graph looks like this: = (a)…

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Q: 6. For how many values of n will a regular n-sided polygon have interior angles with integral degree…

A: For an n-sided regular polygon, the sum of interior angles is n-2×180 In a regular polygon, all the…

Q: Given below is the information of a saving account, what is the average daily balance for the month…

A: From the given information, We have to find the average daily balance for the month of July.   To…

Q: for a product is given by N(x) = 250-250e-0.5 units, where x is the time in hours after production…

A: The given function of production is Nx=250-250e-0.5x. To Find: The average units of production in…

Q: Show that the lim (x,y) → (0,0) √16x² + 9y¹² 4x² + 3y6 does not exist.

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Q: 8. Determine the number of paths from A to B if you can only move Right and Down.

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: Show that, If M and N are nbds. of a point p, then M∩N is also a nbd. of p.

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Q: A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…

A: Given: The given equation of surface is z2+2x2+3y2=4. To Find: The surface integral on the upper…

Q: Define the force field ₹(x, y, z) =. Let S be the portion of the plane z = 2 - 2x in the first…

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Q: (ii) Let K={(), (1 2), (3 4), (5 6), (1 2)(34), (1 2) (5 6), (3 4) (5 6), (1 2)(3 4)(5 6)} with the…

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

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Q: Obtain the Z transform of 10 s(s² +s+2)

A: We are given the Laplace transform fs=10ss2+s+2=51s-s+1s2+s+2=51s-s+12s+122+722-12s+122+722 So,…

Q: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Let S be the surfaced defined by the vector function R(u, v) = , u € [0, 2], VE [-1, 1]. a. Find an…

A: These are the problems from Vector Calculus.

Q: The area of the surface formed by revolving - the curve x = 2√/1 − y in the interval 0 ≤ y ≤ 1 about…

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Q: Given polar curves C₁: upper half of the circle r = 4cose C₂: petal of rose r = cos(40) above the…

A: It is provided that: C1 is the upper half of r=cosθ and C2 is the petal of r=cos4θ. We need to…

Q: Assume that the following determinant calculation is correct. 1 0 0 2 1 2 1 3 0 0 4 1 1 2 5 0 = −32…

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Q: Consider the polar curves C₁ and C2, where: C₁ is the upper half of the circle r = cos 0. C2 is the…

A: It is provided that: C1 is the upper half of r=cosθ and C2 is the petal of r=cos4θ. We need to…