Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2= ($₁292) → (x{₁ > Y&₂) 2 are linear.

Q: The linearization at a=0 to √2+5x is A+Bx. Compute A and B

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Q: The DE (2- y?)dæ- aydy 0 is of the form %3D Select one: dy a. F(ax + by + c) and nonlinear in y. %3D…

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Q: 1. Let F(x, y) = 25x³ + 120x²y + 192xy? + 102y³ – 300x – 450y. Find the following: | ƏF (i). OF…

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Q: 2. Consider the following quadratic form; F(x,y) = ax? +2bxy + cy. Examine under which conditions on…

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Show that Q.) J′′0 (x)=−J0(x)−x−1J′0(x).

A: Here we have to show that, J0''x=-J0x-x-1J0'x

Q: function.   r​(t)=(square root)t+4i + (t/t+9) j−e^

A: We fneed to find the derivative

Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

Q: xy If z show that: x- y

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Q: Let X1 and X2 have the joint PMF f(x1,x2) = x1x2/36 for x1 = 1,2,3 and x2 = 1,2,3. Find the PMF of…

A: Let X1 and X2 have the joint PMF f(x1,x2) = x1x2/36 for x1 = 1,2,3 and x2 = 1,2,3

Q: 1. Evaluate 2dw а. 5-4w-2w2

A: a) Evaluate: ∫2dw5-4w-2w2

Q: Find a such that the distance from (−1, 2) to ax − y + 9 = 0 is √5 units.

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Q: Let r = x² + y – z and z³ – xy + yz + y³ = 1. Assume that x and y are independent ar is variables.…

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Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

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Q: Suppose that TЄ L(R²) is given by T(x, y) = (x + 2y, −y), and consider polynomials p(x): = = x² + 1…

A: (pq)(T)=(x2+4y−4)2+1Explanation:

Q: 1. Find fr (1, 1) and fr (1, 1) where f(x, y) = 6√/2x4 + y³ − 2x+5xy.

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Q: The complementary function (C.F) for the (D² + 8²)y = 0 is O None O Yc = C,cos8x + C2sin16x O Yc =…

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Q: ≤

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Q: If R= [0.1] x [0, 1]. calculate In[(x + 1)(y + 1)]dA. 0 B. 2ln 4-2 C. O D. 1 A. In 4+2 B. 2ln 4-2

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Q: Let u(x, y) = x² - y² and v(x, y) = x³ - 3xy². Show that u and v are harmor functions but that their…

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Q: Let I = S (8x + 10y + 4+ 12xy) dA where R = [0, 1] × [1,2]. R Find I

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Q: Show that for constants a and b ‡ 0 (a) Mx+a(t) = eªt Mx (t); (b) Mbx (t) = Mx (bt); (c) Mx+a (t) =…

A: Solution-: We want to show that for constant a and b ≠0 (a) MX+a(t) =eat MX(t)  (b) MbX(t)=MX(bt)…

Q: d d Calculate ri(t) · r2(t)] and [ri(t) × r2(t)] first by differentiating dt the product directly…

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Q: If f(x, y) = xe"y – In(xy), then dxðy Select one: A. x² ye"Y + 2xe" B. x² ye®y – 2xe™y С. О D. x²…

A: f(x,y)=xexy-ln(xy)

Q: Classify each of the following equations as to order and degree: a. 3dy + (4xy - secx) dx = 0 b. L…

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Q: Given that F′=f, use the substitution method to show that ∫f(ax+b) dx=1aF(ax+b)+C, for nonzero…

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