Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3, g(x) = 2x + 3 -

Q: Find the derivative of the function. (x) = (2x – 7)“(x²+ x + 1)5

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Q: Find the polynomial P1(x) = a0 + a1x whose value and slope agree with the value and slope of f(x) =…

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Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: Calculate R3 and L3 for f(x) = x² - 6x + 6 over [1,4].

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Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Find the linearization L(x) of the function f(x)=x to the 4th power +2x to the 2nd power +1 at x=2.…

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Q: Let f(x) = v9x+ 8 and g(x) = x+9 be functions from R to R. Find the following. a) (f • g)(x) = %3D…

A: We are given f(x)=9x+8 and g(x)=x+9 and we need to find different composition of the function.

Q: Let t(x) = 2x - 1 and m(x) = x² - X. Find m(t(x)) Be sure to simplify your answer. Use the fx button…

A: Given, t(x) = 2x-1, and m(x) = x2-x m(t(x)) = m(2x-1)

Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Calculate R3 and L3 for f(x)=x2−4x+5 over [1,4].

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Q: Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are…

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Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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Q: Find yy as a function of xx if y′′′−8y′′−y′+8y=0 y(0)=4,  y′(0)=−6,  y′′(0)=130.

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Q: Let ƒ(x) = (2x + 3)(3x2). Use the product rule to find ƒ′(x).

A: Consider the formula for product rule. Product rule: fg'=f'⋅g+f⋅g'

Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.