Which function has a remainder of 18 when divided by (x- 2)? Select the correct answer below: g(x) = x + 4x² - 10x – 10 g(x) = 2x + 4x² - 10x- 9 %3D g(x) = x +4x² - 10x - 9 %3D g(x) = 2x + x2 - 9x – 10 O g(x) = 2x +4x2 - 10x - 10 %3D

Q: 4. For the functions f (x) = x + 2 and g(x) = x² – 2x + 7, which expression has the greatest value?…

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Q: Determine the value of k such that when f(x)=x* - kx +7x-6 is divided by x - 2, the remainder is 4.

A: We have to find the value of k. To solve this problem we will use 'Remainder theorem' which states…

Q: Find (f- g)(x) when f(x) = 7x - 8 and g(x) = 2x - 2. O A. - 5x +6 О В. 5х-6 ОС. 9х -10 O D. 5x - 10

A: fx=7x-8gx=2x-2To find:f-gx

Q: Find the inflection points of f(x) = –x* + 24x² + 5x – 4.

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Q: 7. When the function f (x) = 6x* + 11x – 22x² + ax + 6 is divided by (x+1), the remainder is -20.…

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Q: Find f'(x). f(x) = 2 In (2+7x2)

A: Taking derivative with respect to x,   Take the constant 2 out of the brackets,

Q: If f (x) = 4x + 3x2 - 5x +20 and g (a) = 9x - 4x2 + 10x- 55, what is (g-f) (x)? 13x – a2 + 5x – 35 A…

A: See the details solution in below

Q: 1. Find the range of values of x for which y = x3 + 5x2 - 8x + 1 is increasing.

A: We have to find the range value of x

Q: Calculate f""(−1) for f (x) = 3x5 − 2x2 + 7x−2.

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Q: If f(x) = 2x^2 - 3 and g(x)=2x^2+3x-5 , find 3g(-x) 0 f(x^2 -1)

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Q: Given the function y = x2 + 10x + 21, what is the least possible value of y? %3D

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Q: Find the values of k for which f(x) = kx3 -9kx2+9x+3 is increasing on R

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Q: The function f(æ) = 2x³ – 27x? + 48x – 7 has two critical numbers. The smaller one equals and The…

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Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

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Q: Find f'(a). f(x) = 3x2 – 4x + 1

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Q: Consider the function Aa4 –2x²+11 f (x) 3x2 – 2x4 For what value of A does f (x)have 6 as a…

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Q: When the qiven function f(x) = cx^3 - 3x^2 + dx - 4 is divided by (x+2), the remainder is -34. When…

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Q: Find fg.f(x)=5- x²,g(x) = x² + 4x – 12 %3D fg)(x) = x - 4x³ + 17x² + 20x – 60 %3D (fg)(x) = -x*- 4x3…

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Q: Find-f(x) when f(x) = 3x+4x+4. O A. 3x-4x-4 O B. -3x-4x-4 OC. ОС. 3х- 4х +4 O D. -3x -4x+4

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Q: If f(x) = x2 + 3x -10 and g(x) = x2 - 6x + 8, find (f/g)(x)

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Q: Find the f'(x) of f(x) = -2x³ + x⁴ + 2 over 3

A: Given:  f(x)=−2x3+x4+23 To Find: f'(x)=?

Q: Find the slope of f (x) =e8x-10 at x-1.

A: The function is given by fx = e8x-10 The point is  x = x0 = 1 Formula: The formula to evaluate the…

Q: If f(x) = 2x - 5x + 2 and g(x) = x² – 2x + 3, find (f - 8)(x) and (f – g)(3). %3D

A: Given: fx=2x2-5x+2gx=x2-2x+3 To Find:  f-gx=? and f-g3=?

Q: Find the interval of increase of p(x)=x2+5x+6

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Q: If f(x) = x-5 and g(x) = 3x2-1, what is (f° g)(x) ? %3D

A: The given functions are:fx=x-5 and gx=3x2-1To find f∘gx

Q: 8) Find 4 given : f(x)=- (3x² – 2x +1)'

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Q: Let  ƒ(x) = 6x2 − 2 and g(x) = x2 − 2x + 5 to find the value. ƒ(t + 1)

A: Given: fx=6x2-2gx=x2-2x+5 The objective is to find the value of ft+1

Q: The equation that does not represent a polynomial function is Oy = - = -x + Oy = x 10 - x + √22 + x…

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Q: 3. Find the domain of the following functions: 7x2- 5x- 2 (a) f(x) = x2+ x- 6 g(x) =/2r2+ 5x+ 3 (b)…

A: We have to find the domain of the following functions - (a) f(x) = 7x2-5x-2x2+x-6(b) g(x) =…

Q: find the value of (k) to continue the function x²-3x2-4x+12 f(x)={ * * 31 x-3 x = 3.

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Q: What is the leading co-efficient of. 6x -9 f(x) = 1 x ²³² 4 +

A: If y = ax^2 + bx + c  than leading coefficient is a

Q: S(x) = x³ – 3x² – 3x + 1

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Q: Describe the long run behavior of f(r) = – 5r° + 2r - 3r2 + 3

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Q: and g(x) : 3x-1 f (x) = 7 x-3'

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Q: Find the range of values of x for which y = x3 + 5x2- 8x + 1 is increasing.

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Q: find f'a f(x) = 4x2 − 3x + 1

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Q: Find the domain of the function  f(x)= In(x^2+5x+6)

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Q: Let f(x) = x² + 2x − 1 and g(x) = 2x − 4. Find 3f (x) - 2g(x). 2x²2x14 Option 1

A: Solving

Q: Find the domain of the function. 3x 5) g(x) - 6) x2 -1 Vx-2

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Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Find (fog)(4) when f(x)=-2x^2+3x+1 and g(x)=2x-5 If f(x)=2x+7 and g(x)=2x-8, find (fog)(8)

A: a)Given,

Q: If f (x) = 3x + 2 and g (x) = x² - x, find the value. %3D 8(-3) =

A: Given query is to find value of g(-3).

Q: Calculate R5 for f(x) = 4x² + 8x over [-1, 1].

A: The given function is, f(x)=4x2+8x The interval is [-1,1] that is, -1,-35,-35,-15,-,15,15,15,35,35,1…

Q: Consider the following. 7x g(x) - x + 2x - 3

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: 2) Find the domain of the function. 7 – 4x f(x) = 3x + 2

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Q: For what values of x is y = 150x - 2x3 an increasing function?

A: For the function to be increasing the derivative of the function should be greater than 0

Q: Consider the function f(x)=x^3+4x^2−25x−50. If there is a remainder of 50 when the function is…

A: We have to find the value of a

Q: For what value of k will the function g(x)=x^4+kx^2 have a remainder of 20 when divided by the…

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Q: or what value of X does the function g(x) = 1/3 X3 - 2x2 attain the point of inflexion?

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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.