Use the inner product < f, g >= = f(x)g(x)da in the vector space Cº[0, 1] to find < ƒ,g >, ||f||, |19||, and the angle Of between f(x) and g(x) for f(x) = -5x² - 6 and g(x) = −9x + 5. (f,g) = ||f|| = ||g|| 0fg radians.

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

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Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Use the function to find the image of v and the preimage of w. T(V,, V2) = (v, + V2, V - v2), v =…

A: Linear transformation: Let us consider a mapping T:V→W defined as T(v)=w where v∈V and w∈W [  v is…

Q: Find the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

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Q: Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, –…

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Q: (c) If f is a C² scalar function, then V × (Vƒ) = 0. True False (d) The lines 1₁ (t) = (1 − t, 1+ t,…

A: (C) If c is scalar function Means      curl(grad ƒ)  is = 0   Therefore correct ans is  True

Q: F(t) = (Cos(Tt), - 1), G(1) = (1, 1, – 1), G'(1) = (2, 3, 2) , Ĝ"(1) = (0, 1, 0) . (F.G) 1) (Gxở)…

A: Given :- F →t =  cos πt , e2t-1 , t2 - 1  , G →1 =  1 , 1 , -1G' →1 =  2, 3, 2G'' →1 =  0 , 1 , 0…

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

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Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

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Q: f L{f(t)} = y(s), then L{ƒ'(t)} = sy(s) + y(0) y(s) - y(0) s²y(s) sy(s) - y(0) خبار 2 الخيار رقم 1

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Q: Prove that the vector given by (sin ysinh x + cos ycosh x) i + (cos y cosh x- sin ysinh x) j is a…

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Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

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Q: Arsingment (Diff Calculas 4 RoSingle Int.) Ini O n a plane AABC, find the maximum value of cos A cos…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at…

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Q: Given the vector: j(x) sin(2x) X = X ,ex, 1-√1+x (2, 1,-2), x = 0 Determine its domain and show it…

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Q: Given V = {(x, y) |x>0} where (21, 31) (x2, Y2) = (x₁x2, Y₁ + y₂) and co (x, y) = (xe, cy), which…

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Q: Use the function to find the image of v and the preimage of w. T(V1, v2) = (Vị + v2, V1 - V2), v =…

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Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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