A rectangle has the base on x-axis and its upper vertices ile on the parabola y-21-x². The largest possible area of the rectangle is equal to utumia Answear

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Q: 4. What is the equation of the line that passes thru (4,0) and is parallel to the line x-y-2 = 0.

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Q: n=1 11" (x − 4)"(n+1) n+ 11

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Q: -2 -3 8 8 Let A ₁ 1₁ - ( -3² -1²³), and 4₂ - ( 2³₁ - 2 ) be = = 5 -1 -5 two matrices in M. 22 Choose…

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Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: 12. Find a) L-¹ [24+25 s²+25 + $²-9 10 b) - L -2)³

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Q: Find the complex form of the Fourier series f(x)=e*, -1<x<1 Ans. E

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Q: Ο Σ n=1 (-5) " 32n

A: I have used simple trick of geometric sum.

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Q: Find the surface integral of the field F(x,y,z)=yi-xj+5 k across the portion of the sphere x² + y² +…

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Q: The differential equation for which sin¹x + sin¹y = c is given by: O √1-x²dy+√√1-y²dx = 0 O √1-x²dx…

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Q: 4. Solve the linear equation systems 2x, +5x₂+2x, = -8 by using Crout method, where (x₁+2x₂ + 3x₂ =…

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Q: Which of the following is the even periodic extension of the function f(x)=3x9-x²+x³-4, 0<x<L with…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 3y + 2y = 8(t-5)+uo(t),…

A: The given Initial Value problem is                          y''+3y'+2y=δ(t-5)+u10(t)  ,     y(0)=0,…

Q: c) f(t) = sin tet d) f(t) = sin t

A: Leatgt=Fs-a Lgtt=∫s∞Fudu where  Lg(t)=Fs

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Q: If an infinite seriesak diverges, then the infinite series a must diverge. n=1 n=1 (x+1) k k=10…

A: Both the statements are FALSE. We shall give counter examples to both the statements which have been…

Q: Determine whether S = {1-1,2t +31², 1²-21³,2+1³} is a basis for P3.

A: DEFINITION OF A BASIS-: A SET OF VECTORS v1,v2,v3,.......vn IS SAAD TO BE BASIS FOR A VECTOR SPACE V…

Q: Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that 3 is an…

A: Given: A binary relation ≡3 on ℤ defined by x ≡3 y if x-y is divisible by 3. (a) To Prove: ≡3 is an…

Q: QUESTION 22 (Analytic geometry) A conic section is the figure formed when a plane intersects a cone.…

A: Visualise by drawing as follows

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Q: 5. Determine the half range Fourier cosine series for -{- f(x)= 7-X

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Q: Evaluate the integral of ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

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Q: Suppose is a simple closed piecewise smooth positively oriented curve, and let D be the region…

A: Given: Multiplicity of zeros N=5. To find: Multiplicity of poles.

Q: B. f(t) = t³ >= {₁² 0 0 sit 2

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Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

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Q: Let A = 15 0 13 2 x = 1 - 12 and b = 3: 15 25 73 Define the linear transformation T: R² → R³ by →…

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Q: If f+g is are differentiable at x0, then prove f and g differentiable at x0 ww

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Q: Let α₁, ₂ and B₁, B₂ be the roots of ax² + bx + c = 0 and px² + qx + r = 0, respectively. If the…

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Q: 0 t3 B. f(t) = (10) = {² 0 sit 2

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Q: 1. Substitute z = 1-2-y in problem (1) to obtain an equivalent unconstrained optimization problem…

A: As per the question we are given the following nonlinear optimization problem : min (x-2)2 + (y-3)2…

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Q: Write general solution of 2x²y" + 5xy' + y = 0. Answer:

A: LET  x=ez⇒z=logx and D1=ddz so that xD=D1 , x2D2=D1(D1-1) SO GIVEN EQUATION REDUCES TO,…

Q: Prove using mathematical induction. Show your solution. Prove 3 + 7 + 11 + … + (4n – 1) = n(2n + 1)

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

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Q: pns called digraphs. By determining which vertices should be red, green, and blue, give a proper…

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Q: Your supervisor asked you to run more studies on the AirTag. You need to make sure that each…

A: Part(a)Supervisor asked you to run more studies on the AirTag. You need to make sure that each Air…

Q: Consider the following differential equation to be solved by the method of undetermined coefficients…

A: Given: y''+2y=-18x2e2x To find: (a) ycxb ypxc yx