1 Find (fog)(x) when f(x)= x +5x+6 and g(x) = x+3 O A. 5x+36x2+81x+55 2+6x+9 O B. 1 2+5x+9 O C. x+2 O D. 6x2 +41x+70 x2+6x+9

Q: Graph the following functions.

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Q: 1-х 26. f(x) =- х+2 27. /(х)- Vx* - 3

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Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

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Q: 4. Given that (fog)(x)3= 4. and f(x) = Sx+4 9x-2 Determine g(x). Hence, find g(0)

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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: 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: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

A: Note:- As per the company guidelines we can solve first question. I hope that the given solution…

Q: Derivatives of quotients Find the derivative of the followingfunctions.

A: "Since, you have posted a question with multiple subparts, we will solve the first three subparts…

Q: 11. If f(x) = 15 -g (x) for -2 <x < 2, then If(x)– = - (x)] dx : %3D (A) 2 g(x) dx – 60 | -2 ~2 (B)…

A: Consider the given function. fx=15-g(x) in the interval -2≤x≤2. The objective of the problem is to…

Q: 19) 1+ V3 mult. 2 A) f(x)= x* – 7x' + 8x + 4 B) f(x) = x* – 4x³ + 7x² + 8x + 4 - - 3 = x* + 4x' + 8x…

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Q: 8. Find (S+gx). f)- Sx - 9x + 8 g(x) - &r - 7x +2 A) (+ gKx) - 13 - 16x + 10 B) (+ gXx)--3r-2r +6 C)…

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Q: 6. y = xe* 7. y= 3x.e* 8. y = x² In(x) 9. y =x*(5x – 1) 10. y = (x² + 2x)5(3x-3 +x²)-7 11. y = (1 –…

A: Use product rule of differentiation.

Q: 2 Find [f(x) + 5g(x)]dx if 2 |f(x)dx = 8 and / g(x)dx = -1. -4 [f(x) + 5g(x)]dx = i -4

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Q: Bind/x(n) X(n) if XCZ) Z² (Z-1) (Z-0.5)' Z² N

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Q: The function f(x)=2x^3−24x^2+72x−2 has two critical numbers. The smaller one equals=     and The…

A: We have to find critical numbers  First we have to differentiate of f(x) with respect to x  After…

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: 1.) f(x) = x² + 2x g(x) = 2x - 3 Find (g - N(x) 2.) f(x) = 2x' + 4x + 2x + 1 9(x) = x' - x + 7x + 9…

A: Explanation of the answer is as follows

Q: 5. f(x) = 2x - 6 x2 - 7x + 12 Holes: Vert. Asy: Hor. Asy:

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Q: x2n+1 El-1)"; 2n +1 n=0

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Q: 2.8 The antiderivative of the function f(x) 5 is -7.9 + 0.7x +c | -2.8 + 2.0x + c -2.8 .0 + 2.0x3 +c…

A: Need to find antiderivative of f(x)

Q: Evaluate: x/9x2 + 4 (A f (x) = -4 ln V9x2 + 4 + 2 +C f (x) = - In 4 V9x2 + 4 + 2 + C 3x © f (x) = -2…

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Q: 13. If f(x) = 3x -4 the equation for f¹(x) is 0y=x+3/ 3 Oy=1/x+³/ Oy=4x+3 Oy=3x+4 4

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Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

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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: 2. If f(x) = x-1 and g(x) = - x2+ 2 a) Find (fog)(x)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (x -1, if 0 < x < 1 2x f(x) = |x – 3| , g(x) = -4 Vx, h(x) = %3D , if

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Q: 19. f(x) = x - 4, g(x) = Vx + 5, x 2 -5 %3D

A: Consider the functions f(x) = x – 4, g(x) = √(x + 5), x ≥ –5

Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: 3) Ar) = VF g(x) = V-(r + 2) – 3 4) Ax) = VF g(x) = - Vx + 3 5) Ar) = Vx g(x) = -2 Vx - 1 6) Ax) =…

A: We have to find translation

Q: 3) g(x) = x + 2 f(x) = x³ + 4x Find (g · f)(x) А) бх* - бх3 + бх? - бх 2x + 4x2 – 8x 4) f(x) = x² –…

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Q: I'm studying for a precalculus exam and I want help on this problem because I am stuck.

A: Given that,

Q: 2. Find all critical points. 1 a) g(x) = (x² – 1). b) f(x) = x³ + 6x² – 15x.

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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: 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: 3) Given that f(x) = 2x + 5  g(x) = 2x - 6   and h(x) = x2 - 5…

A: This is a problem related to function and inverse function. Based on the general formula we will…

Q: Find the x values of the two critical points of: 3(x- 1)23 6x – x² - 5 if x > 2. if x < 2 f(x)%3D X…

A: we have the given function is ;  f(x)=3(x-1)2/3if x≤26x-x2-5if x&gt;2

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: ) Given that f(x) = 2x + 5  g(x) = 2x – 6 /  x and  h(x) = x2 – 5  Find:- i) f(-4) = ii) h[f(-6)]…

A: Function value and it's composition

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: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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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: In Problems 37–48, determine algebraically whether each function is even, odd, or neither.

A: 37. A function f(x) is even if f(x)=f(-x) for all x in the domain of the function. A function is…

Q: 11. f(x) = Vx² – 9 = V x-2 12. f(x) X-1 13. f(x) = Væ² – x – 2 - if æ > 0 14. f(x) = -2x, if x < 0.

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Q: Find (5x - x²)e* dx O(x2 -5x)e-x-(2x - 5)e¯X – 2e-*+c O (5x-x2)e*- (5 – 2x)e* +2e* O (x2-5x)e*- (2x…

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Q: In x +1 If y = then will be 2x³ – 3x' (2x³ – 3x) G+1) – (In x + 1)(6x² – 3) (2x — 3х)? А. (2x3 — 3х)…

A: SOLUTION-

Q: 1. f(x) = 3x^3 -2x^2 -4x +1; g(x) = -5x +6x^3 -2 +x^2 . Find (g-f) (x). * %3D -3x^3 -3x^2 + x +3 O…

A: Given: f(x)=3x3-2x2-4x+1g(x)=-5x+6x3-2+x2 To find (f-g)(x)

Q: 1. g(x) = 2 + x – x² , find f'(-3) H 2. f(x) = 4x, find g(2x) 3. g(x) = x° – 14, find g(3) 4. g(x) =…

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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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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.