4: Which of the following functions has gradient vector [4x₁x₂ 2x² 3x²]¹? A: f (X) = 2x{+2x3+x3x3 B: f(x) = 2x²x₂ + x² C: f(x) = 2x²x₁ + x² D: Non of these O A О в О с O D

Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

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A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: 4 2 IF Ø = 2x2² - xy₁ FIND 01111 AT THE POINT (2-2,1)

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Q: The range of y = v16 – x² is А. [4, со) В. (4, оо) C. [-4,4] D. [0,4] Е. (0,4)

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Q: 9. Determine an expression for the gradient of f =Y x+y

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Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: A3. Consider the function of two variables u(x, y) = xy² — x¹ — —⁄7y³. du (a) Compute and ди ду (b)…

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Q: дz x² + y², x = 2x + 3t and y = s + t. Find and in two ways: Ət Let z = x дz əs (a) By Chain Rule.…

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Q: 40. The algebra rules for gradients Given a constant k and the gradients af. Vf = дх -i + af af k,…

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Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2,…

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

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Q: 1 g(u) = V5и + 8 then g' (u) =

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Q: f(x) = x³ - 5ex + 7x Find the first 2 values of the derivative vector when the derivative of the…

A: Given: The function, fx=x3-5ex+7x.   To Find: The first 2 values of the derivative vector when the…

Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(6) = −4, g'(6) = −8,…

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Q: af Let f(x, y) = x³y + 8. Compute (1, 2) and -(1, 2). ax ду

A: Given: fx,y=x3y+8

Q: Which of the following is a stationary point of the function f(x, y, z) = x² – 2y? + yz + 2ay – z…

A: Given f(x,y,z)=x2-2y2+yz+2xy-z

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Q: Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its…

A: 1) Given information: x¯1 = 7x1 - 5x2x¯2 = -5x1 + 4x2 The components of contravariant in xi…