Find the value of b such that f(x) = Vx + 1+2 has inflection point at x = 3.

Q: Find all values of x such that dy/ldx = 0 where y is the function stated below. x2 y = -3x + 4)

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Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: Find the value of c that satisfies the MVT of f(x) = 1+x + x2 on (0,2).

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Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

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Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: Find the linear approximation of f(x) = e(a) at a = 1.

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Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

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Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: Find the linear approximation to f(x) = at a = 4.

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: For f(x, y) = 2y3 + x² – 4x – 4xy – 9, find the critical points and use the - Second derivative test…

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Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

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Q: Find the linearization of the function f (x) = x6 at x = 1. L (x) = Using this linearlization, f…

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Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: Find the orthogonal trajectories of x^2+y^2−2cy=0

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Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

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Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: Find the linear approximation of f(x) = Vx at xo = 27.

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Q: The function f(x, y) = 2xy + yx + 11 has two critical points. Select one: True O False

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Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: 2 f(x, y) = x² + 3xy

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Q: Find the antiderivative of the function: f(x) = ex + 3x - x2

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,