For items 1 - 2. Let f (x) = 3x² + 9x – 3 and g (x) = 4x³ – x² + 4x – 9 %3D 1. Determine (f – 9) x. 2. Determine (f+g) (2) . For items 5. Let f (x) = 9x² + 7x – 3 and g (x) = –4x – 1 - 5. Determine (fg) x.

Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.…

A: Given: fx=4-x2, fx=x2-16, fx=x-12 We know that any given functionfx is increasing in a interval if…

Q: 26. g(x) = 3x+ 4 %3D 5. f(x) = (x + 3)² – 5 for x<-3

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Q: 3) g(a) = 2a- 1 4) f(x) = x+4 %3D h(a) = 3a -3 Find (g.h)(-4) h(x) = 5x-2 %3D %3D Find ()(2) 5) f(x)…

A: we need to find multiplication and division of functions

Q: In Problems 21–32, tell the maximum number of real zeros that each polynomial function may have.…

A: "Since you have asked multiple questions we will solve the first question for you. If you want any…

Q: x-2 Given f(x)= 3x-8, g(x)= 5x', h(x)=- find: 3 %3D 3. g (x)-f(x) 4. f(g(x)) 5. h(g(S(2)))

A: (3) g(x)-f(x)=5x2-(3x-8)g(x)-f(x)=5x2-38x+8 (4) f(g(x))=f5x2f(g(x))=3(5x2)-8f(g(x))=15x2-8

Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

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Q: 9. f(x)= 3x-4; vertical stretch by factor 4 %3D 10. f(x) = |x- 3; 3 units left then 2 units up

A: (Question 9) We have to write the new function g(x) after the transformation of the following…

Q: 9. f(x) = x3-8 %3D at x = 2 x-2 10. f(x)= (x+2)(x+3)-12 ,at x = 1 x-1

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Q: f(x)=−2x^5-9x^-7 + 10^3√x what is the antiderivative of f(x)?

A: Given query is to find the antiderivative of f(x).

Q: If f(x)= x - 4 and g(x)= Vx-2; which of the following is equal to х — 2 Option 1 – 4(SF 2) X - х — 2…

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Q: 1) If f(x) = - 2x, then f' (8) = A) B) D) 1 E) 3 3x -2 2) If f(x) = , then f'(x) = 2x+1 A) 2 -7 B)…

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Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

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Q: 1. f(x) = 5x² – 7x – 17, find: (a) f(2), (b) f(-2). (c) f(x + 5), (d) f(x – 3). 2. f(x) = 3x³ + 6x²…

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Q: f (x) = x³ + 2x² + 6x e Z¡[x] g(x) = x* + 4x + 5x + 6 e Z¬[x] O x+ 4 O None O x +1 O 2r + 1 O x + 2

A: f(x)= x3+2x2+6x Taking x common, we get f(x)=x(x2+2x+6) [ For (x2+2x+6),…

Q: if f(x)+g(x)= 3x +2 and g(x) = x - 1 then f(x)= %3D а. 2х+3 O b. 3x+2 О с. 3х-2 O d. x+4

A: Given,f(x)+g(x)=3x+2g(x)=x-1f(x)=?

Q: A) xy' 2y + x'e*

A: These are all unrelated &amp; lengthy problems. By Bartleby policy I have to solve only first one.

Q: dæ Evaluate: x/9x² +4 A) None of the above V9x² + 4 + 2 B f (x) = -2 ln +C %3D 3x © s(12) = -- In f…

A: I=∫dxx9x2+49x2+4=t9x  dx9x2+4=dtdx=9x2+49x dtI=∫19x2 duI=∫1u2-4 duI=∫1(u-2)(u+2)…

Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

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Q: Let y=(x^(2)+x+1)^(5)(x^(3)-1)^(2). Then (y')/(y)equals (a)(5x-5-6x^(4))/(x^(3)-1)…

A: Solve the differential equations

Q: 2x +1 40. f(x)

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Q: Find the linearization L(x) of f(x) 5x2 5x + 5 at x х — 2. a) L(x) 15x 15 O b) L(x) 25x + 15 c) L(x)…

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Q: - 15. f(x) = x° (x =3)' (x +1) f(x) = -3x(x-2)'(x-1) 16. HE 17. f(x) = 4x°(x-1)° (x+2)

A: The given polynomial function are: 1. f(x)=x2x-32x+1 2.fx=-3xx-22x-13 3.fx=4x3x-12x+2 We have to…

Q: find the value of k so that the remainder is R when f(x) is divided by (x – r):   f(x) = 2x2 + 3kx…

A: Since, you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

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Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

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Q: If 0.3 is added to 0.2 times the quantity x − 3, the result is 2.5. What is thevalue of x?

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Q: 3. If f(x)=-4x+2 and g(x)=vx 8 find (fog\l12) 4. If f(x)=-3x+4 and g(x)=x find (gof)(-2) 5. If f(x)…

A: 3. Given f(x)=-4x+2 and g(x)=x-8f∘g(12)=fg(12)so now substitute g(12) in given…

Q: . for the following Suppose: h(x) = 4x3 + 5x² + 2 and f(x) = 3x – 5 %3D

A:

Q: 1.a. Determine the values of a and b for fx) =-2x + ax+ bx+ 6 so that f"(-2) = 0 and f"(7) = 0. b.…

A: fx=-2x3+ax2+bx+6 Differentiating w.r.t x- f'x=-6x2+2ax+b Then,…

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

A: Please refer to the image below

Q: 3. f(x) = (3x – 2)* %3D 4. f(x) = (x² + 1)° (xr? – 1)² | (2x – 6)* f(x) = (x + 7)7 5. -2 6. f(x) =…

A: See the details solution in below

Q: 5х - 1 хр- x2-3x-40 a) O 3ln)x - 8| + 2ln/x + 5| + C b)O 4ln|x - 8- 21n/x+5 C c) 3In)x+8 + 2ln/x -…

A: Consider the given function as∫5x-1x2-3x-40dx

Q: 1. Find fog. f(x) = -4x + 6 A) (f°g)(x) =-5x B) (fog)(x) =-4x² + 30x – 36 C) (f°g)(x) =-4x + 30 g…

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Q: The function f(x) = 2x³ – 27x² + 48x 1 has two critical numbers. - The smaller one is x = and the…

A: We have to find the critical points for the function f(x)=2x3-27x2+48x-1.

Q: да Given zTan¯¹ (x + y) — ln [1 + (x + y)²] = 5%, what is ду -1 2-2x-2y none of the choices 2- 2x +…

A: ∂∂xtan-1x=11+x2 Note : As per our Guidelines , we can solve first question. Please repost remaining…

Q: 5 Find (f(x) + 5g(x)]dxif -5 5 5 | f(x)dx = 8 and g(x)dx = -4. -5 -5 5 f(x) + 5g(x)]dx = i -5

A: The given integral values,∫-55fxdx=8 and ∫-55gxdx=-4

Q: If (x) = g(x) + 7 for 3< x < 5, then Lf(x) + g(x)] dx = b. 2 f, g(x) dx + 14 d. 2 g(x) + 28 a. 2…

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Q: Derivatives of the sum of functions Find the derivative of thefollowing functions

A: We have to find the derivatives of following functions: 19. fx=3x4+7x20. gx=6x5-x21. fx=10x4-32x+12…

Q: -8 f(1) – 4 g(4) =[ %3D 8- 6+ y= f(x) 2+ -8 -6-4 6. -4+ y=g(x) -6+ -8- ఈ

A: Given, The graph of the functions  y=fx   and  y=gx We have to find the value of expression…

Q: 8. 8. 8. If f(x) dx = 35 and g(x) dx = 12, find [4f(x) + 5g(x)] dx. %3D

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Q: If  8 f(x) dx = 31   0  and  8 g(x) dx = 12,   0  find  8 [2f(x) + 3g(x)] dx.   0

A: we have to find

Q: 21. g(x) = 2x* - 20x + 18 22. f(x) = 3x* - 15x + 12 23. F(x) = Vx – 1 25. f(x) = 1 -/3 -8 27. G(x) x…

A: Given that: g(x) = 2x4 -20x2 +18. And G(x) = -8/(x2 + 1) We find relative extrema of both function.…

Q: dæ Evaluate: 9x² + 4 A None of the given choices B f (x) = -4 ln 9x² + 4 + 2 + C f (x) = -2 ln 9x2 +…

A:

Q: The antiderivative of the function 6. + 8x is. x2 f(x) -6 + 16.0x² + c -6 4.0x? + c - 6 4.0x2 + c -…

A: Solving

Q: 3) If h(x) = 3x –4 f (x ) = 4 x + 6 g (x) = - 2 x- 4 Composition of functions а. h(5) b. g (h ( 5))…

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

Q: 1 Evaluate f x(x + 4)3dx OA) 3/7 (x+4)^(4/3) (x-3)+C

A: using substitution method to solve.

Q: Given: F(x) = 5x - 6 and G(x) = x - 4 G -1 F -1 = (x + 26)/5 -6x + 10 (x + 10)/5

A: The value of G-1o F-1 is (x + 26)/5

Q: 4. Suppose f(1) = 5 and f'(1) = 3. Let %3D 3.a-5x2 h(x) = 2f(x) +1 Find h'(1).

A:

Q: 2. Let f (x) = 6 – 2x, g (x) = Vx + 6 , and h (x) = 3x² + 4 Find the indicated values. %3D A) (f +…

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Q: dæ Evaluate: æ/9x² + 4 9x2 + 4+ 2 + C V A f (x) = -4 ln 3.x f (x) = -2 ln V9x2 + 4 + 2 + C None of…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.