1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis and between the lines x = -1 and x = 1, illustrated below. -1.5 1 -0.5 2 y = x² + 1 0.5 1 1.5 (a) Use n = 4 rectangles and left endpoints for each rectangle to estimate the shaded area. Notice that you cannot be certain whether this estimate is an overestimate or an underestimate because some rectangles miss shaded area and other rectangles include unshaded area. (b) Use n = 4 rectangles and choose your sampled point to guarantee that you get an overestimate of the shaded area. (c) Use n = 5 rectangles and choose your sampled points to guarantee that you get an underestimate of the shaded area.

Q: Assume that it costs that same company approximately C ( x ) =62,229+5,573x +0.033x 2 dollars to…

A: The given cost function is Cx=62,229+5,573x+0.033x2. It is known that, the average cost function can…

Q: Assume that it costs that same company approximately C(x)=71,230++6,670x+0.03x^2 dollars to…

A: Given data-  C(x)=71,230+6,670x+0.03x^2. We have to find the average cost function= C¯(x).

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: 1. Below is the graph of a function y = f(x). Estimate the area underneath the graph over [-3, 3]…

A: Since, you have posted multiple questions, but according to guidelines we will solve first question…

Q: 8) Sketch the function with the zeros (x + 3) (x=1) (x= 2)and: the y-intercept of -6. After doing…

A: To sketch the graph of the given function.

Q: 7/8 For what value of x does the graph of f(x) = x8e* have a horizontal tangent?

A:

Q: Calculate G' (-4) to 3 significant figures where G(x) = (-4x – 2)'°(-2x² + 1x + 4) 2

A: Calculate G'(-4) to 3: significant figures  G(x)= (-4x-2)10(-2x2+1x+4)12

Q: Assume that it costs that same company approximately C() =67,822+4,195x+0.05x2 dollars to…

A: Given,          The cost function is Cx=67822+4195x+0.05x2 dollars to manufacture x of…

Q: A company finds that the marginal profit, in dollars, from drilling a well that is x feet deep is…

A: Total profit is integration of marginal profit

Q: 8) Sketch the function with the zeros (X+ 3) (x+ 1) (x -2) and the y-intercept of -6. After doing…

A: Given: Given that the function (x+3) (x+1)2 (x-2) To Find: To sketch the given function

Q: Suppose that f(x) is a linear function. So, the algebraic representation of f(x) is of the form:…

A: The algebraic representation of the linear function is fx=mx+b

Q: 3. When compared to f (x) = e*, how does the graph of h(x) = -e**3-4 x+3 differ? A Vertical stretch…

A: Consider the functions  f(x)=exh(x)=14ex+3−4

Q: Graph the functions in excercise

A: Solution:Giveny=9-x

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A: Integrate marginal revenue and get total revenue

Q: 3. For which function is the average rate of change over the interval 1 < x < 5 greater than the…

A: To find- For which function is the average rate of change over the interval 1 &lt; x &lt; 5 greater…

Q: A manufacturer has determined that the weekly profit from the sale of x items is given by the…

A:

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Given graph is as follows where the red graph shows f(x)  and a line tangent to the curve at x=4.…

Q: The magazine Scientific American released a study of data analysis on how quickly children are able…

A: The function P(t) represents the percentage of children who can speak in at least single words by…

Q: 15) Match the graph with the correction function. (a) (x) = 4' - 5 (b) S(x) = 4' + 5 (c) (1) = 4-X +…

A: (a).    The given function is: f(x)=4x-5

Q: Assume that it costs that same company approximately C(x) =62,229+5,573 x+0.033x2 dollars to…

A: Given, C(x)=62,229+5,573x+0.033x2 where x be the improved deluxe gameplay stations in an hour and…

Q: Find k such that the line is tangent to the graph of the function.

A:

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x – 3x + 229, where x…

A:

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01² - 3x +229, where a…

A:

Q: 36 Complete the following table for the function y 0.5 1 2 3 Click on the graph below, and use the…

A: y = 36/x

Q: Find k such that the line is tangent to the graph of the function.

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)

Q: 18. Suppose that a company produces and sells bicycles and that the start-up cost is $3000 and $75…

A:

Q: b. Based on the graph of f(x), will the slope of the normal line drawn to the graph of f at x=4 be…

A: Given: The function is fx=2x-3cosx. To show: f'x=1+3xsinxx Differentiate with respect to x:…

Q: Suppose that the function y = f(x) is decreasing on the interval [ - 2, 7].(a) Over what interval is…

A: Given: Suppose that the function y = f(x) is decreasing on the interval [ - 2, 7].

Q: The marginal cost function for the manufacture of wireless headphones is given by C'(x) = 34 −…

A: Given: Marginal cost function is given as:

Q: If the marginal revenue (in dollars per unit) for a month for a commodity is MR = -0.6x + 43, find…

A: Given query is to find the total revenue function.

Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: 3. Find the exact area of the piece of land in San Francisco, Surigao del Norte which is bounded by…

A: Topic:- application of integration

Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A:

Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

A:

Q: Find k such that the line is tangent to the graph of the function. Function= f(x) = k square root x…

A: Find k such that the line is tangent to the graph of the function. Function= f(x) = k square root…

Q: 14х y = Зх-6

A: Given:   To determine: excluded x value for the function.

Q: The cost C of building a house is related to the number k of carpenters used and the number x of…

A: The solution for the above question is as shoewn below.

Q: 4. Identify and sketch the graph of three distinct level curves of the function. f(x, y) = Ln(y –…

A: Given that the function fx, y=lny-3x. We have to sketch the graph of three distinct level curves of…

Q: 46. The following equation is used to calculate the aver- age firing rate f of a neuron (in spikes…

A: The equation fx=20e3x2.1+e3x is used to calculate the average firing rate f of a neuron (in spikes…

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

A:

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x² – 3x + 229, where a…

A: Given : C(x) = 0.01x² - 3x + 229 and        R(x)  = 429 - 2x

Q: With U.S. Department of Energy data for selected years from 2000 and projected to 2030, sulphur…

A:

Q: Find the level curve of the function at c=2 for g(x,y)=(x^3-y)

A: A scalar function g(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A: Given   Marginal revenue function X = no. of gadgets R’(x) = thousands of dollars   R’(x) = 4x (x +…

Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01x² – 3x + 229, where…

A: Given that: Cx=0.01x2−3x+229Rx=429−2x To find the area between the graph.