Find fe(), the Fourier series expansion of * € [-L, 0), * € [0, L], where k and L are positive constants.

Q: High school swimming state averages are as follows: Freestyle: mean time 72.39 seconds, standard…

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Q: 4. (a) If X is an infinite dimensional space, show that the set {x = x | || x || = 1} is not…

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Q: 2. A toy rocket is launched from the ground and the arch can be modelled by the following equation,…

A: Given function of height is  h = 19- 0.4(t-7)^2 Where t is time after launching in second.

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. 34 49

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Q: Determine whether it is possible to multiply the following matrices. If​ so, what is the dimension…

A: We know that For matrix multiplication, number of columns in first matrix is equal to number of rows…

Q: Use the Green's Theorem area formula, Area of R = - 2 C r(t) = (-5 cos ³t)i + (-5 sin ³t) j such…

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Q: Find the following matrix product, if it exists. -1 1 - 1 3 -4 1 4 -2 -5 -2 0-1 Select the correct…

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Q: 1000 7. If a rectangular fence is supposed to have 3 pens, and in total enclose feet find the…

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Q: onsider the functionf:R→Zgiven by the floor formulaf(x) =⌊x⌋.(a) (7 points) Isfinjective? Explain…

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Q: 3. Letf(x)=x² +3 and g(x)=x³-1. Use the standard inner product on C[0, 1] to compute the following:…

A: Let X be the vector space over the field F. Then, the inner product on the vector space X written as…

Q: Use the Green's Theorem area formula, Area of R = 1/ 4x dy dy-y dx, to find the area of the region,…

A: We have to find the solution by Green's theorem.

Q: H.W solve by picard method (up to third approtination) c =X+y² y (0)=0 Find y (0-1)? dx aus/ "Y3…

A: Picard Iteration method :  yn(x)=y0+∫0xf[t,yn−1(t)]dt here we have f[x, y]=x+y2

Q: B. Find the area of the region bounded by the following: r = 8 sin 1²/1/20 16.

A: The given curve is r=8 sin2θ2 To find : The area under the curve.

Q: 1. Find the domain and range of the following: 1 (a) f(x, y) = = y-x² (b) g(x, y) = 9 - x² 2 (c)…

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Q: f(x) = e²x cos(x)

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Q: Obtain the Laurent series with center zo = 1 for Determine a) The singularity/ies of the function b)…

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Q: Show that Z6 is isomorphic to U(7) by giving an isomorphism φ from Z6 to U(7).

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Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D 34 49

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Q: nd sine half range for f(x) = \cos x for -1<x<1 COSX for 7<x< 0. f(x) COSX for 0 < x < π.

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Q: Find the Fourier series for the given function. f(x) 9 200 f(x) ) = ²/²2 - ²2/2 2² 1 2m ² - 1 ² (2m…

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Q: Suppose you want to have $500,000 for retirement in 20 years. Your account earns 4% interest. How…

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Q: 1+2 e-kt cos kx = k=1 sinh t - cosht cos x

A: To prove / disprove: 1+2∑k=1∞e-ktcoskx=sinhtcosht-cosx

Q: (a) Let R be a ring. State the definition of a zero-divisor of R. (b) Find the zero-divisors of the…

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Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

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Q: Find all the generators tof the subgroup H = (2) in Z24-

A: In any cyclic group of order n has phi(n) generators. We use this technique to solve the problem.…

Q: 4) Let the function f be defined as f(x) = sin(x) for all x. An example visualization is shown in…

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Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

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Q: View Policies Use the ratio test to determine whether the series converges. If the test is…

A: To use the ratio test to determine whether the series converges.

Q: a² + 8a + 15 6a² +21a +9 )( a-4a 2a²+9a-5

A: Given expression is a2+8a+156a2+21a+9a-4a32a2+9a-5

Q: EAT has been selling their very own Platinum Eco-Charger since the beginning of this semester. If…

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Q: Problem 2: Let P₂ be the space of polynomials with R coefficients of degree ≤ 2. Consider the…

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Q: Suppose G = (a) is a cyclic group of order 6. Find all the subgroups of G and list the elements in…

A: We have to find all the subgroups of G and list the elements in each of these subgroups.

Q: What is the equation of the graph shown? 20 18 16 14 12 10 8 6 4 2 0 -2 -4 -6 0 2 -8 -10 -12 -14 -16…

A: We will start with a basic graph and then transform that to the graph given , Correspondingly…

Q: Find the Fourier series for the given function. 9 f(x): = 200 Σ πm=12m-1 2 9 f(x) = 9 - 1¹ 2₁ πm=IM-…

A: Given function is f(x)=9, -L≤x&lt;00,     0≤x&lt;0 with period 2L Let the Fourier series be…

Q: QUESTION 13 Let F(x,y,z)=x²zi+yj-xz²k Find the curl of F. O a-1 Ob.1 Oc_x²-2² Od. x² + z² O ex² - 2²…

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Q: letT: R³ R³ be the linear operator defined by T(X₁ X2 X3) = (X₁-X2, X2-X₁) X₁ X3) - a Find the…

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Q: 2. (a) Let X = C[0, 1]. Define T: X→ X by. Tf(x) = xf(x) Show that (i) T is bounded (ii) Find || T…

A: Given- Let X = C0, 1. Define T : X → X by Tfx = xfx.  To Show- Show that T is bounded. Find T.

Q: * Evaluate. 2t |4 + et| dt

A: Solution :-

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, I 2

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Q: E1: Obtain the forward, backward, and central difference for du/dx for the function u(x,y) = 2ye-*…

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Q: Let X and Y be random variables with joint probability density function -x-y f(x,y) = {ety for…

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Q: * Evaluate. [6x² arcsin(x)]dx

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Q: 3 1 (6) Consider the system z'= Ax + G, where A = and G(t) = (a) Decouple the system using the…

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Q: Find the flux of F = 5zi+ 3y²j+ 2xk through of the total surface of the closed cone y = Vx² + z²,…

A: Flux of vector F through a surface S  can be given by  flux= ∫∫SF.ds We will use Divergence theorem…

Q: -x Let F(x, y) = (e + 4y)i + 8xj. Evaluate the integral Jo F. dr, where - C is the boundary of the…

A: Given- Let Fx, y = e-x + 4yi + 8xj.  To find- Evaluate the integral ∫CF·dr, where C is the boundary…

Q: A manufacturer sells each of his TV sets for $85. The cost C(in dollars) of manufacturing and…

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Q: Compute ||w| using w= ||w|| || = 7 5 -4 (Type an exact answer, using radicals as needed.) LO

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Q: evaluate the integral where c circle of positive rotation e^z/1 -cos(z) dz where C is |Z |= 1

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Q: Prove using partitions that Explain this result geometrically. ·b cb+c [ f(x) dx - [bte f(x = a+c…

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Q: 010 = Let R₁ and R₂ be relations on a set A represented by the matrices MR₁ 1 1 1 and MR₂ = 100 ГА В…

A: Given that R1 and R2 be the relations on set A represented by the matrices…