Use the intermediate value theorem to find the value of c such that f(c) = M. %3D f(x) = x2 – x + 1 on [2, 12]; M = 13 C =

Q: Find the antiderivative F(x) of f(x)=x/3(12x2-6), given F(1)=5

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: Find the particular antiderivative that satisfies the following conditions: F' (x) = a* + 5Væ; F(1)…

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Q: Consider the function f(x) = 4x – 7x² + 9x – 10. Ca2 An antiderivative of f(x) is F(x) = Ax* + Bx -…

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Q: Evaluate the given function using homogeneous x- yArctan () dx + xArctan () dy = 0 A. 2yArctan ()…

A: We need to find solution of differential equation using homogenous.

Q: Differentiate the following with respect to x: c) Vx2 + 1

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Q: given f(x,y)=ex^3 . y^8-x8y3 ,show that fxy=fyx

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Q: Let f(x) = e3x-5 a. Find an expression for dy. b. Estimate dy for x = 2 and dx 0.04

A: To find an expression for dy Also to find the value of dy at x=2 and dx=0.04

Q: Evaluate f fs 2² dS, where S is the portion of x2 + y² + z² = 2 in octant 1.

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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.

Q: Find the antiderivative F(x) of f(x)=x(2x+7), given F(4)=5

A: Given:The function is f(x) = x(2x+7), F(4) = 5.

Q: Find the value of C such that the fnction Continubus on (-00,00) Cx +1 for XS 2 f(x)= r4x+I-3 for…

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Q: If L(x)=mx+b is the linearization of f(x) 2x-x +3 at x-1, then m3 Using L to approximate 2(1.01)…

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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: Let f(x) = 4x - 8x. Find F(x), the antiderivative function, if F(1) = 3.

A: Let f(x)=4x2-8xTo find the antiderivative function F(x)if F(1)=3

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: Find the general antiderivative of f(x) = 4x – 5. Use Cfor the arbitrary constant. nswer F(x) =

A: Fx=∫fxdx

Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? O -2 O -1

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Q: (a) If e19z f (2) = z10 + 49 at how many points the function f (z)is discontinuous ?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: let x has the p.d.f (11e-11x 0 < x< ∞ 0. W f(x) = Find m.g.f and prove that E(x) = M,(0)? %3D

A: We want to find the Mx(t) and E(x)

Q: Please show step-by-step solution!

A: According to chain rule the derivative of the f(g(x)) is [f(g(x))]’=f’(g(x)) * g’(x)

Q: (a) Find the linearization L(x) of f (x) = v25 – x² at a = 3. (b) Use the linear approximation L(x)…

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Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: of Find and for the following function. f(x,y) = e Y In (3y)

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Q: Q2: Let f(x) = 2x e-,x> 0 and Let Y = X2.Find G(y)and g(y). %3D

A: Implicit functions are the functions are not directly expressed, these are always expressed in terms…

Q: ) Find the local linear approximation of the function f(x) = V1+x at xo = 3, and use it to…

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Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Given the function, f(x) = √x + x, use linearization at x = 4, to approximate f(4.1)

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Q: Find the linear approximation to f(x) = 1 and then use that to approximate close to 1.003 1 1.003

A: Given: The function fx=1x To find: The linear approximation to fx=1x close to 11.003, then…

Q: Find constants c1 and c2 such that: G(x) = c1xe^−x + c2e^−x is an antiderivative of g(x) = 3xe^−x.…

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Q: If F(x) is an antiderivative of x2 + x*1, then what is the value of F(1) - F(-1)? O -1 O 3 O -2

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Q: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: Consider the function f(x) = 4x10 + 5x° – 5x² – 8. An antiderivative of f(x) is F(æ) = Ax" + Bm +…

A: F(x) is the anti derivative of f(x) , so to find F(x) we have to integrate the given function f(x).…

Q: Consider the function f(x) = 5x³ 8x2 + 5x – 3. An antiderivative of f(x) is F(x) = Ax* + Bæ³ + Cx² +…

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Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? 3 -2 O -1

A: Solved below

Q: If F(X) is an antiderivative of x2 +x', then what is the value of F(1) - F-1)? (А) -2 В) -1 D) з

A: Given: F(x)=∫x-2+x-1dx So, by the Fundamenetal theorem of calculuas: F(1)-F(-1)=∫-11x-2+x-1dx Now,…

Q: Consider the function f(x) = 2x + 3x" – 7x² – 4. An antiderivative of f(x) is F(x) = Ax" + Bx" + CaP…

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Q: Consider the function f(x) = 6x° – 4x? + 2x An antiderivative of f(x) is F(x) = Ax* + Bx³ + Cx² + Dx…

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Q: Consider the function f(x) = 5x-5x2 +4x 8. An antiderivative of f(x) is F(x) - Aa* + Ba + + Cx? + Dx…

A: The given function is: f(x)=5x3-5x2+4x-8

Q: Consider the function f(x) = 2x° + 4x" – 8x² – 8. An antiderivative of f(x) is F(x) = Ax" + Bx™ +…

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Q: 4. Find the linearization L of the function f(x)=Vx+3 at a = 1 and use it to approximate f(x) =…

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Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: Consider the function f(x) = 8x - 8x2 + 4x – 3. An antiderivative of f(x) is F(x) = Ax* + Bx + Cx² +…

A: We have to find antiderivative of f(x) or integral of f(x).

Q: Consider the function f(x) = 6x10 + 7x – 5x² – 5. An antiderivative of f(x) is F(x) = Ax" + Bx" +…

A: Antiderivative is called as integration of a function. Integration gives the function whose…

Q: Let F(x) be the antiderivative of F ‘(x) = -2x + 6, with constant 0.  Determine F(x), and then…

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Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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Q: If L(X)=mx+b is the linearization of f(x)=2x³ – x +3 at x-1, then m= 1.625 Using L to approximate…

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Q: Consider the function f(x) = 5x³ – 2x2 + 5x – 9. An antiderivative of f(x) is F(x) = Ax4 | Ba + Cx2…

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