Consider F and C below. %3D 1 + x2 i+ 2y arctan(x) j F(x, y) C: r(t) = t2 i + 7t j, osts 1 (a) Find a function f such that F = Vf. f(x, у) 3D

Q: Let F(x) = f(x°) and G(x) = (f(x))" . You also know that a = 9, f(a) = 2, f'(a) = 8, f' (a") = 9 %3D…

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A: The given function is fx,y=x9+3y9+7. Evaluate fx as follows. fx=∂∂xx9+3y9+7fx=9x8 Thus, fx=9x8.…

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A: As per the guideline, I am supposed to solve only first question from the given problems.

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A: To find the direction in which the function is increasing most rapidly.

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A: The objective of the question is derivative of given function and choose the correct option.

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Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

A: Given the following functions                  f1(x)=sin(x1)cos(x2),   x∈ℝ2f2(x, y)=xTy,   x, y∈ℝn…

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A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: Find fa(x, y) and fy(x, y). f (x, y) = (y" tan(7æ)) fa(x,y) : fy(x, y)

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Q: Pls help ASAP

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A: According to our company policy we are supposed to answer only first question. For the rest please…

Q: a) Find the directional derivative of the function f(x, y, z)=x² y² (2z+1) at the point P:(1, -1, 1)…

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A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Find f f(x, y) dA where f(x, y) = x and R= [5,8] × [-3,2]. SSR f(x,y) dA= Preview My Answers Submit…

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A: Answer is mentioned below

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Q: F(x, y, z) = (2xz + y²) i + 2xy j + (x² + 6z²) k C: x = t²2, y = t + 2, z = 2t - 1, 0≤t≤1 (a) Find a…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.