The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the y-axis.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Use the Midpoint Rule with  n = 4  to approximate the area of the region bounded by the graph of…

A: Given:    Approximate using mid point rule:∫04x2+4x dx ,  n=4

Q: Determine the area of the given region. 1. Region between f(x) = x - 3x – 4 and the x-axis from x =-…

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Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

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Q: Find the critical numbers and identify the points for the absolute extrema on the given interval.…

A: Critical numbers are the values of which satisfies f'(x)=0 Given f(x)=x3-12x , [0,4] f'(x)=0 gives…

Q: 3. Find the exact area between the curve f (x) = -2x² + 12x + 7, the x-axis, and x=1 and x=5.

A: As mentioned, use the sigma formula to find the area A. Plot the curves. Divide the area between the…

Q: Find the absolute maximum and minimum values of f(x,Y) = Zx(y-1) + 7 on the region above the line…

A: We have given f(x, y) = 2x(y - 1) + 7. Method of Lagrange Multiplier:  To find the maximum or…

Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

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Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 5x + 8y on the…

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Q: Let f(x, y) = x² - y² + 2y. Find the absolute maximum and minimum values of f on the region 4x2 + y²…

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Q: 65. The region bounded by f(x) = x² and the x-axis on the interval [1, 0) is revolved about the…

A: We have to find the volume of the described solid of revolution.

Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

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Q: The area of the region between the x-axis and the carve y = e¯ -3x for x >0 is

A: Formula:For y=fx; y≥0 area between the curve y=fx, x=a,x=b and x-axisA=∫ba fxdxGiven y=e-3x

Q: 2. Find the absolute maximum and minimum values of f(x, y) = 4x+6y-(r²+y?) on the rectangular region…

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Q: The area under the curve y = Vĩ bounded from below by the 16 x-axis and on the right by x = 4 is…

A: Integration can be used to find area of region bounded by a set of functions. For two functions…

Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: Find the absolute maximum and minimum values of f (x, y) = 4xy – x* – by the line y = -2 above by…

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Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

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Q: 4. Find the absolute maximum and minimum of the function on the given closed bounded region. y…

A: Given function is fx,y=ex2-4x-2y+y2 Closed region is x=0,y=0 and x+y=3 The objective is to find the…

Q: Find the absolute maximum of f(x,y) = 3x2y2 + 2y2 + 2x2 bounded by y = x, y = 0 and x = 5.

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Q: Find the extreme values of the function f (x, y) = e¬¤y given that (x, y) must live in the region…

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Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: The region bounded by f(x) = tan x and the x-axis on the interval [0, 7/2) is revolved about the…

A: Volumes of Solids of Revolution: - Revolving the region bordered by y = f(x) and the x-axis on the…

Q: Find the global minimum of the function f (x) = 1+x² on the interval (-∞, 0) . Write DNE is there is…

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Q: The total area bounded by the graph of y =r 2. 1 and the x-axis is represented by

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Q: 2. Find the absolute extrema of the function on the closed interval. f (x) = Vx – 2, [0,4]

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Q: Find the area of the region bounded by f(x)=X^2-4X +3 the X axis in the lines X=2 and x=6

A: We will find out the area of the region.

Q: Find the maximum and minimum attained by f(x, y) = 3xy + 2x + 3y in x2 + y < 1. You must use…

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Q: Find the absolute maximum and minimum values of f(x, y)= 3+xy-x-2y on the closed triangular region…

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Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular…

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),…

Q: Locate the absolute extrema (maximum AND minimum): f(x) = 10x(2 - lnx) ,  on the interval [1,e^x]

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Q: Find the extreme values of the function f at the region of x2 + y² = 4 where: F (x, y) =x² + 2y²-2y…

A: The extrema of the function can be calculated by calculating the derivatives of the function. First…

Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

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Q: The area bounded by the curve y = 3/x and the lines x = 3 and x = 8 above the x axis - is _square…

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Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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Q: Find the area between the curve f(x) = −3x^2 + 3 and the x-axis over the interval [−1, 2].

A: Answer and explanation is given below

Q: 2) Find the absolute maximum and minimum for function F(x,y)= 4x³-2x²y+y² on the region R bounded by…

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Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 9 -x, and the line perpendicular…

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Q: Find the absolute maximum and absolute minimum values of the function f(x,y)=x2+y3 on the region…

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Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"

Q: Find the absolute maxima and minima of the function on the given domain. 6) f(x, y) = 6x + 5y on the…

A: f(x,y) = 6x+5yfx(x,y) = 6     fy(x,y) = 5  (Hence No critical points of the function itself)Lets…

Q: Find the maximum value of J (x) f(x) = V1 + x² on the indicated interval. [0,2]

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Q: Find the area bounded by the curve f(x) = x³ + 3x² – 4x – 5 and x-axis from x = -3 to x = -1 using:…

A: Consider the given area bounded by the curves as y=x3+3x2-4x-5 and the x axis from x=-3 to x=-1. Let…