f : M₂(F) → F defined by f(A) = det(A) is a ent to B then det (B) = det(A).

Q: consider a function f, defined by f(x,y) = -y/√x2+y2   what is the behavior of f along the line…

A:

Q: Let f: Z → Z where f(x) go f(0) = fog(-3) = go f(x) = fog(x) = = x² + 6. Let g: Z → Z where g(x) = x…

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: true or false :  There exists a function F of two variables x, y such that dF = (x − y)dx + (x +…

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Q: Find the Green's function G" + k²G = 8(x − s), Gʻ(0, s) = 0, G′(0,π) = 0 -

A: To find the Green's function G(x,s) for the given differential equation G′′+k2G=δ(x−s), subject to…

Q: If h and f are functions and g defined by g(t) = f(t) · h(t), then what is g'(t)? f'(t)h'(t) +…

A: We have given that gt=ft·ht Differentiate the above function w.r.t 't' g't=ddtft·ht

Q: The domain of the function g(t) = vt – 2 is O R-{2} O [2, 00) O R о (-о, — 2) n (? m)

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Q: Find f∘f where f(x)=3x−5 and f: ℝ→ℝ

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Q: Let the invertible function Evaluate f(x) = 3x³+x+3 1 = ["] † ^¹ (2²) dar dx (Hint: You may use the…

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Q: Use the table to determine Df(g(x)) at x = 3. |1 2 f(x) 1 3 4 3 2 f(x) 3 -5 1 4 g(x) 2 4. 4 1 3…

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Q: Determine fr and fy from f(x, y) = x³ + x²y + xy² + y³ ○ fx = x + xy, fy = x + 2xy ○ fx = x² + xy,…

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Q: . Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |<a < }; 1, 21 (a) Show that f € R([0,…

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Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Solve the given initial value problem using the method of Laplace transforms. 5, Ost≤7, y" + 2y' +…

A: One has to solve using Laplace Formula:

Q: Suppose f(r) z2 + sin z and F is an antiderivative of f that sausfies F(T) 0. Then F(2) = ( -1)

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Q: What is T3 centered at a = 3 for a function f such that f (3) = 9, f' (3) = 8, f'' (3) = 4, and f'''…

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Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

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Q: Let f(x) = x – 5, g(x) = /x , h(x) = x°, and j(x) = 3x. Express each of the functions given below as…

A: The solution of above question is written in below steps.

Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: Let h=f∘g where f:R2→R and g:R2→R2 is defined by g(x,y)=(−3x2y,3x+3y). Find the derivative h′(1,2)…

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Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

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Q: Find all functions f : Q to Q satisfying (i) f(1) = 1 and (ii) f(x+y) = f(x) + f(y) for all x,y \in…

A: we  have to find the required function.

Q: 1. Let f : (−1,1) → R, f(x) = (1+x³)-³. Compute g' : (0, 1) → R where (a) g(x) = X X f. (b) g(x) =…

A: Answers along with explanations are provided in the image. Explanation:

Q: Let f(y) be the function such that S f(y)dy=y In (4 + 9y²) + C. 1 Evaluate f 4x f(x² + 1)dx.

A: Calculation of Required Value.

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (1) and s'(4). y…

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Q: f (x, y) = 6xy² for 0 <x<1 and 0<y<1 and f (x, y) = 0 Calculate fx (x) and fr(y) Ny looking at the…

A: If x and y are two continuous variables then f(x,y) is called joint probability density function.…

Q: 2 Iƒ ƒn(x) = efn−1(x) for all ne N and fo If d nd {ƒn(x)}. dx

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Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Let T : R3 → R* defined by T(v,. Vy, 2,vg) (3, Vz, v1). Find T’(v) and T10° (v)

A:

Q: 6. Let f be a function such that f(1) = 1, ƒ′(1) = 4, ƒ”(1) = −2 and ² ƒ""(t)(2 – t)²dt = 3. Find…

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Q: Consider the functions f: Rx RR and g: R→ RX R given by f(x,y) = x -y andg(x) = (x,x²) Find the…

A: Given function are f:R×R→R and g:R→R×R defined by fx,y=x−y and gx=x,x2. We have to find the formula…

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

Q: Find all functions f:R → R that satisfy the equality xf(y) + yf (x) = (x+ y)f(x)f(y) %3D for all r,…

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