PROBLEM : Determine the area bounded by the curves f(x)z 20a + 32 and a(r) 10+ 16. Answer: Area : A square units (Use the calculator and write your answer to 3 digits after decimal point)

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 a cubic function y = ax + bx2 + cx + d whose graph has horizontal tangents at the points (-2,…

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

A: Given, R(x)=429-2x C(x)=0.1x2-3x+229 Graph

Q: Find the absolute extrema of the function f(x, y) = x + y + 3.ry on the closed region bounded by the…

A: Absolute Maximum and Absolute Minimum

Q: A bowl has a shape that can be generated byrevolving the graph of y = x2/2 between y = 0 and y = 5…

A: The Volume of the bowl is given by

Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

Q: Find the equation of the image when y = -x+2 is reduced with scale factor of 2/3 centered at (1 ,…

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Q: an equation of the line tangent to the function of x2 + (y – x)2 = 9 at x = 1.

A: At given value of x find y Differentiate at given value Use equation of tangent line

Q: 6. Find the point on the curve y = yx that is closest to the point (3, 0)

A: let P is the closest point then say (x,y) then find the distance from the point (3,0)  then minimize…

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

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

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Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given y=e-x2

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01a? number of cell phones, and…

A: First graph the curve and their intersection point. In the graph we can see clearly that…

Q: (i) Find the values of k for which y= kx + 2 is a tangent to the curve y= 4x2+ 2x + 3.

A: If y = kx +2 is tangent to the curve y=4x2+2x+3, then the point of intersection of the line and the…

Q: A factory selling cell phones has a marginal cost function C(r) 0.01x represents the number of cell…

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Q: 4. What is the slope of the curve of f(x) = v2x + 1 at x = 4? а. 3 b. - с. d. ! e. None of the above

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

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

A:

Q: Solve the problem. Find where the tangent to the curve f(x) = V+1 that has slope . O x = 3 O x = 1 O…

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 3 the point (2, 2.8).

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Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

A: The curve is given by the equation, y=x99+128x7  and the point is given from x=1 to x=2. To find :…

Q: 3 Find a cubic function Y= ax²³²+ bx tcx td whose graph has horizontal tangents at the points (-2.4)…

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Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

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Q: 49. Find an equation of the tangent line to the graph of y = 8/(x² + 4) at (a) (0, 2); (b) (–2, 1).

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Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x-axis ? OA…

A: what is the slope of the line tangent to the curve x2+y2=1 and parallel to the x axis

Q: 41. Aroller coaster has the shape of the graph in Figure 19. Show that when the roller coaster…

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Q: Find each of the two areas bounded by the curve y = x³ – 4x and y = x² + 2x. Solve in two ways.

A: Given curves are, and Comparing both,

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: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

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Q: 8. Find the constant "k" such that the slope of the tangent to y = 12e-2.3x+k is equal to -4 at x =…

A: 8. Given Data: The equation of the line is: y=12e-2.3x+k The slope of the tangent to the given line…

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

A: Consider the given equations as follows. Cx=0.01x2-3x+229Rx=429-2x Let us find the area by…

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

A: SOLUTION-

Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: 5. Find each of the two areas bounded by the curve y = x3 – 4x and y = x² + 2x. Solve in two ways.

A: Consider the two curves: y=x3−4x and y=x2+2x. The area of the region bounded in interval x∈a,b by…

Q: QUESTION 15 Find the area bounded by the curve y = 16 4 square units 16 square units 10 square units…

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Q: = -x2-2x+2 and C(x) x2 + 0.5 = 4 C(X) R(x) 1 -2 -1 1 2 The profit, or the area enclosed between the…

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Q: 19. For what value of h will the line y =-2x +h be tangent to the parabola y = 3x +4x-1? (4T) b)…

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Q: If the length of the curve y = 4 x7 from the point (0, 0) to the point (Xo, f(xo)) is L= 1 (145)*…

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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: In submarine location problems, it is often necessary to find a submarine's closest point of…

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Q: 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 %3D = - 3x2 f(x) = 4…

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Q: Sketch the graph and show all local extrema and inflection points.   y= -x^4 + 4x^2 -6

A: If a function is f(x), then 1. For extreme points, f'(x)=0. 2. For inflection points, f''(x)=0.

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

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

Q: 10. Find the points of inflection of the curve y f(x)=x³ -x.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the points at which y=f(x)=x^9−17x has a global maximum and minimum on the interval 0≤x≤4.…

A: To determine the global maximum and minimum.

Q: C(x) = 5x; R(x): 8x – 0.001x? %3| Find all values of x for which the marginal profit is zero.

A: Given : Cost function, C(x)=5x Revenue function, R(x)=8x-0.001x2

Q: Does the graph of S0, x< 0 U(x) = 1, x2 0 have a vertical tangent line at the point (0, 1)? your…

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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.

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Q: A factory selling cell phones has a marginal cost function C'(x)=0.01x^2-3x+229 where x represents…

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