Find a map s: R → R şuch that S(3) s(0) - 1, s(2) + 4s' - 4s = 0, s'(0) −1, - - = s'ʼ(0) = 1.

Q: Write the coordinates of the vertices after a reflection across the line x = 2. F E D -10 10 10 D(3,…

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Q: Let f = 12r + kry + Jryz re-express f O f(r,y,z) = (x, ry, Tyz+) O {r,y) = (x, ry, ryz*) O f(x,y) =…

A: GIVEN f= ix+kxy+jxyz4     ....(1)

Q: What is the composition of the translations (T T) (x, y) as one translation? and q = (T T)(x, y) =…

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Q: Consider the function d: R² × R² → R defined by {} d(x, y) = min{|y2x₂, 1} if x₁ = y₁ otherwise, 1…

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Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

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Q: Let f(x, y, z) = 9xy sin (yz) and F = Vf. Evaluate F · dr, where C is any path from (0, 0, 0) to (5,…

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Q: Consider the function d: R² × R² → R$ defined by [min{\32 - x₂, 1} if x₁ = y₁ 1 otherwise, d(x, y) =…

A: A metric on a set X is defined as a function d: X×X→ℝ which satisfies the following conditions:…

Q: "; Find y as a function of x if x?y" + 5æy' – 21y = x°, y(1) = 7, y(1) = -5. y =

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Q: 2. - For each map below, either prove that it is linear or demonstrate that it is not linear. (a) T…

A: Consider a map T:U→V is linear if    (i) T(u+v) =T(u)+T(v)   (ii) T(αu )   = αT(u)   , for all u,v…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) =i - 3tj + K 2 (a) r'(t) (b) r"(t) (c)…

A: Given that, r(t) = (3t2/2)i - 3tj + (t3/2)k   Ans (a). first derivative of the function, r'(t) = 3ti…

Q: let T: P4(R)→R2 be the map given by T(f)=(f(1),f"'(1)) where P4(R) is the set of polynomials of…

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Q: Graph of f

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Q: Find the functionr that satisfies the following conditions. r'(t) = (1,4t ,5t4); r(1) = (7, – 6, –…

A: Given that

Q: Let F(x, y, z) = (x-1z, y¬lz, In(xy). (a) Verify that F = V ƒ, where ƒ(x, y, z) = z In(xy). (b)…

A: Given Fx, y, z=x-1z, y-1z, lnxy (a) Verify for F=∇f where fx, y, z=z lnxy The gradient of a function…

Q: Let f(u, v) = (tan(u - 1) - ev, u²-v²) and g(x, y) = (ex-y,x-y). Use the Chain Rule to find…

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Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Let f(x, y, z) = x + yz and let C be the line segment from P = (0, 0, 0) to (4, 5, 5). (a) Calculate…

A: Given function is  and let  be the line segment from . We have to calculate  and for , .Since,…