Consider the rational function 2x5 f(x) = 9x4 + 4x3 – 18x² – 28x + 12 2x3 x2 + 6x – 3 where 2x – x² + 6x – 3 = (2x – 1)(x² +3). - (a) Decompose f(x) into partial fractions. (b) Hence find the antiderivative of f(x). You may use the following standard antiderivative result, that we have not studied in the course: 1 1 (:). -1 dx = - tan a + 0. x² + a2 a (c) Find the exact value of | f(x) dx, simplifying your answer as much as possible.

Q: Suppose f(x) = 5x 6 and g(x) = vx² – 4x + 8. %3D - - (f o g)(x) = (f o g)( – 5) =| %3D

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Q: Reduce the fraction to its lowest term f(x)=(0)² - 4(0) + 5/0-4

A: Given a function, fx=x2-4x+5x-4 At x=0, f0=02-40+50-4

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: What is the remainder when f(x)=x3−22x2−16x−161f(x)=x3−22x2−16x−161 is divided by (x−33)(x−33)?

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Q: Find the rational zeros of the function f(x) = x3 − 7x − 6 .

A: Given the function f(x) = x3 − 7x − 6 . We need to find the rational zeros of the function.

Q: Letf(x) = x² – 5x + 6, g(x) = 5x – 1, find the following: (1)(f + g)(x) = (2) (ƒ − g)(x) = - (3) (ƒ…

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Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

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Q: 7 f(x) = 6 x² – 20 x* + 4 find f (4) (x).

A: We have to find 4th order derivative

Q: Find all zeros of f(x) = x* + 5x³ – 2² – 23r – 6. Find all possible rational f(x) = x* + 5x³ – a² –…

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Q: √(√x − 2 csc xcotx + 1) dx is equal to 3 2x 2 3 3 2x 2 3 3 2235734 2x 3 3 2x 2 3 + 2 csc x + ln x +…

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Q: is f(x) = -3x + 4 a bijection?

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Q: Let x) = √3x and g(x) = x² + 2x - 1. Find f. g. (f. g)(x) = x²-√√3x + 2x√3x - √√3x (f. g)(x) = 3x +…

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Q: y(x)=(x+1)2(x+2)3(x+3)4,x>−1.

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Q: Find f(a), f(a + h), and the difference quotient la + h) na) where h * 0. f(x) = 5 - 6x + 2x2 f(a) =…

A: Given,            f(x) =5 - 6x + 2x2

Q: 8. FIND f(4) (x) OF f(x) = 3x7 + 4x6 + 8x³ – 2x + 1

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Q: For f(x)=2x4 +2x3-1 and g(x)=2x3 +2x+3 in Z4[x], the degree of fg is 7. True or false

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Q: Prove WITHOUT using the product property of determinants: If M, N are triangular matrices, |MN| =…

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Q: F(x) 1/ (x-3)(x-5) Find the domian of the follwing fractions. No symplifying the equations.

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Q: Let f(x) = 5x - 4 and g(x) = x? – 5x + 6. Then %3D %3D (f o g)(x) = %3D (go f)(x) = %3D

A: givenf(x)=5x-4and g(x)=x2-5x+6fog(x)=f{g(x)}=f(x2-5x+6)=5(x2-5x+6)-4=5x2-25x+26       answer

Q: u(x)=2-2x + 5x * +7x³ + (x-1)u(t)dt

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Q: Suppose f(x)=√x² + 6x +10 and g(x) = −3x + 9. (fog)(x) = (fog)(-1) =

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Q: If f(x) = - 3/2 and g(x) x + 2 2x² 3 6x + x² 3 6x + 1 1 2x + x² x + 6 2x² = X + 1, find (-1)(x) (x)…

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Q: 2. Find f(g(5)) if f(x) = 2z + 5 and g(x) = 3x2 %3D O f(g(5)) = 675 O f(g(5)) = 155 %3D O f(g(5)) =…

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Q: Find all solutions of the following differential equations: (a +1)ry/ – (d + 1)y= cos y/x a=1, b=6,…

A: Given: a+1xy'-d+1y=cosyx For, a=1, d=6. We have, 2xy'-7y=cosyx …1

Q: uation of the tangent line to ƒ at x = 1.

A: Given that: The equation is f(x) = x2+3x .