Sketch the graphs of the functions. f(x) = −x2 + 3x and g(x) = x − 3   Find the area of the region completely enclosed by the graphs of the given functions f and g.

Q: The region between the graphs of f(x)=x^2+3 and g(x)=−x+5 has ____________area square units.

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Q: Find: (fog)(x) (gof)(x) (fog)(2)    f(x)=7x+1 and g(x)=2x^2-9

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Q: The demand function for a certain product is  p = 121 − x2  and the supply function is  p = x2 +…

A: Solution:  The demand function for a certain product is    p = 121 − x2  and the supply function is…

Q: Find the number of units x that produces a maximum revenue R. R = 66x2 − 0.04x3 x =  units

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Q: 4. The function I results when the function f() = 2x" + 54x" is vertically stretched by a factor of…

A: Given The given function f ( x ) = 2x5 + 54x2

Q: Find the number of units x that produces a maximum revenue R. R = 156x2 − 0.08x3     x =…

A: Simply take the derivative of the given function and make equal to zero than solve for x.

Q: The area of a parallelogram bounded by the y-axis, the line x=6, the line f(x) =6+2x, and the line…

A: The line parallel to y = 2x +6 will be of the form y = 2x + k…

Q: maximum revenue for the revenue function  R(x) = 372x − 0.7x2.  (Round your answer to the nearest…

A: Please refer to the image 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: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?

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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: (b) Complete the table for y=-x + 8x - 7, including all integral values of x such that 0SxS8. This…

A: Make a table for (x,y) and substitute all integral values in the function and find y. x…

Q: Find a function H that multiplies a number x by 3 and thensubtracts the cube of x and divides the…

A: Given : To find the function H such that multiplies a number x by 3 and thensubtracts the cube of x…

Q: Find the x- and y-intercepts for the function. x2 + 4x + 3 x2 + 11x + 28 f(x) x-intercept (x, y)…

A: Consider the function, fx=x2+4x+3x2+11x+28

Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per…

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Q: What effect does the “k” in f(x)= ^3 √x+k have on The graph of the cube root function ^3 √x and…

A: Given the function We have to find the effect of the k in the above function.

Q: Find the area of a triangle bounded by the y axis, the line f(x)=4−(6/7x) and the line…

A: Formula Used: Area of triangle is :                                   Where,  b is base of triangle…

Q: f the profit function for a product is  P(x) = 6400x + 80x2 − x3 − 220,000  dollars, selling how…

A: The profit function is: P(x)=6400x+80x2−x3−220000

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

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Q: Find number of units X that produces a maximum revenue R. R=99x^2 - 0.06x^3

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Q: A​ once-popular children's doll is slowly declining in popularity. The quartic function…

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Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

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Q: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per…

A: Compare the given cost function with the general quadratic function as follows.

Q: During a nationwide program to immunize the population against a new strain of the flu, public…

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Q: the total daily profit of a certain food company for the sale of boxes of buko is given by the…

A: Given: The total daily profit of a certain food company for the sale of boxes of buko is given by…

Q: The region in the first quadrant bounded by the x-axis and f (x) = 3x – x² is

A: The graph of region bounded by curves y=3x-x^2 and x-axis is

Q: Find the general solution for: X' = là X. -3 %3D

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Q: f(x)%3D4×+2x2 - x³ for -5 <x s 5. |

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Q: Find the maximum area of a rectangle inscribed under f(x)=16-x2 and the x axis

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Q: Find the x-coordinate of the absolute maximum and absolute minimum for the function 9. f(x) = 10x +…

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Q: 1) g(x) = 2x + 8

A: given function g(x)=2x+8 on diffrentiating this function we get

Q: The region between the graphs of f(x) = x² + 3 and g(x) = x + 9 has area square units.

A: SOLUTION-

Q: At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a…

A: Given model of the equation is simplified by expanding the brackets:

Q: Find the number of units x that produces a maximum revenue R. R = 66x2 − 0.04x3

A: Explanation and solutions is given below....

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

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Q: Find the area in the first quadrant, bunded by the function, f (x) = 3/x+1 , and x = 4

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Q: Find the number of units x that produces a maximum revenue R. R = 33x2 − 0.02x3 x = _____ units

A: Given R=33x2-0.02x3         Here we find the number of units x that produces        a maximum…

Q: Draw the graph of f ( x ) =3 x2+5 x−4 for a. From the graph, identify the values of x when f (x)=0.…

A: Follow the steps below to plot the graph of y=f(x) . Take arbitrary integers for the values of x…

Q: On what interval is f(x) = x³ + 3x² – 24x +7 decreasing? The graph is decreasing on the interval

A: Use first order derivative test to obtain the interval of decrease.…

Q: Find the maximum revenue for the revenue function  R(x) = 372x − 0.7x2.

A: To Determine :- The maximum revenue for the revenue function. Rx = 372x - 0.7x2

Q: the total daily profit of a certain food company for the sale of boxes of buko is given by the…

A: Given that the profit function is: Px=-0.001x3+0.1x2+3x-300 Then we get,…

Q: find all possible functions with the givenderivative. y' = 3x2 + 2x - 1

A: Definition used -     Function from derivative -         f(x)=∫f'(x)dx

Q: find the maximum revenue for the function R(x)=356-0.9x^2

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Q: Find the maximum profit and the number of units x that must be produced and sold in order to yield…

A: Given: The revenue function is Rx=x2+110x+60. The cost function is Cx=1.1x2+10x+80.   Determine the…

Q: 10) f(x) = V3x – 1

A: Explanation of the solution is given below..

Q: 3. Find the absolute maximum value of f(x) = x³ – 3x² on the interval -15x<3 (A)–4 (B) 0 (C) 1 (D) 2…

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Q: The function f(x) = 12 – 6x4 has an absolute maximum value of and this occurs at x equals

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Q: Find the absolute maximum value of the function f(x) =-z² – 4x – 2 on the interval [3, 3 ]. a) О-2…

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Q: Determine the value of t that maximizes the area above the x-axis and below the graph of the…

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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.