Find the area of the shaded region. 160- (-2,152) f(x) = x* - 8x + 18x, g(x) = - 25x + 102 3,27)

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Q: The area of the shaded region below is f(x) = x- x2 2x -1-

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Q: Зх — 5 f (x) = х+ 2

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Q: • 61. f(x) = 4 – x², x2

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Q: lim V4x + 8 X--2*

A:

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A: we will expand the given function using the formulae, (a+b)2 = a2+b2+2ab and (a-b)2= a2+b2-2ab

Q: (b) Find the area of the region between the x-axis and the graph of f(x) =-x² -2x, where -3<x<2…

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Q: solve

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Q: Find the number of units x that produces a maximum revenue R. R = 78x2 − 0.04x3   x=           units

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Q: B. Qurfient Rule ) f x)= x² 3x²

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Q: f(x) = 4x² + 6x g(x) = 2x² + 13x + 15 oJa) iven find Show your work.

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Q: lim t-→∞ 8 (1²)√42t³ + 25t¹2 + - 7t² t 7835t881t5 + 10t3

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Q: Find the maximum and minimum of f(x, y) = x² + y² - 8x – 18y if x > 0, 0 x. (Use symbolic notation…

A: The solution is given below:

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Q: What is the domain of f(x) = V5 – 4x – x² ? O A.(-5, 1) А. OB. [-5, 1] В. Oc.(1, -5] С. O D. (-1, 5)…

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Q: 6. Given f(x) = -3x*-12x3-7x +3, find f(-2) by plugging into f(x) %3D

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Q: lim 4x? + 1 x→3

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Q: Зх — 5 f (x) = х+2

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Q: Using the definition f'cx) = lin fCxth ) -fw find f'C4) when fex)=-ax² +3x -7 3. ニーa×

A:

Q: The shaded region shown below is bounded by the functions f (x) = -2x² + 0.75x + 4 and g(x) = 1.5x +…

A: The shaded region shown below is bounded by the functions fx=-2x2+0.75x+4, and gx=1.5x+2 and the…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.