If f(x, y) = 3e-2x cos (y – 2), then the linear approximation at (0, 2) is (A) 3 – 3x (B) 3+ 6y (C) 3 + 3x + 6y (D) 3 – 6x (E) 5 - 6x + 3y

Q: The equation of the tangent line for the function f(x) = -7 – 5x at z = 7 is O y = -5(1 – 7)+42 O y…

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Q: Find y as a function of x if X y(0) = −1, y′(0) = 9, y″(0) y(x) = = -16. = y" - 4y" y + 4y = 0,

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Q: If z = f(x) + yg(x), what can you say about zy? Explain!

A: Answer is 0

Q: If f(x, y) = sin(xy+, then fy(0, 1) = X+x3 5 undefined 2 1

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Q: Find the linear approximation of the function f (x, y) x² + y² at the point (2,-1, 1)

A: Given function:- fx,y=5x2+y2

Q: If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

A: Given function is: f(x,y)=xey22+118x2y3 Derivative of function with respect to 'x'…

Q: b) Find all the analytic functions for which Rez = Im f(z)

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Q: Find y as a function of x if y(0) = 10, y(0) = 10, y"(0) = 18. y" - 16y" +63y = 144e",

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Q: Determine the linear approximation of f(x) = x at x = 1. O a. Not in the list О b. у3 3х +2 с. у %3…

A: A detailed solution is given below.

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Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: 3) f(x, y) = -9 sin x-5 cos y at (0, 5 (0,7) A) L(x, y) = 9x - 5y - C) L(x, y) = -9x - 5y - 5 B)…

A: We have to find the linear approximation of the given function.

Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

A: The given function is, fx=-3-6x We need to find the equation of the tangent line to the function at…

Q: = x³y² – 3x²y + 5x – 3y + 12

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Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: Determine whether linear or nonlinear:  y(t) = -jt*x (t) y(t) = j+x (t)

A: A linear equation is the one in which the highest degree is 1. A non-linear equation is an equation…

Q: Find y as a function of a if y(0) = 5, y(0) = 17, y"(0) = 5, y"(0) = 8. y(x) = y(4) — 6y" + 9y" =…

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Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: If f (x, y) = x²y² + sin(xy) then fy (2,0) = 2.2

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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Q: The function f (x,y) = x3-6x+2xy+y2+2y+6 has two stationary points. Find and classify then.

A: The  given function  is  We  have two first find two stationary  point  of the given…

Q: ? ? ? 1. f(t) = 4t² + 28t, g(t) = 4t² - 28t 2. f(0) cos(30), = g(0) = -8 cos³ (0) + 6 cos (0) 3.…

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Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

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Q: Show that f(z) = elmz is nowhere complex-differentiable.

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Q: Let A be a positive constant. The equation of the line tangent to the curve sec(y) + x³ - 9 = Ay at…

A: Equation of tangent to the graph y=f(x) at point x1,y1 is given byy-y1=dydxat x=x1,y=y1×(x-x1)   The…