Describe a region whose signed area is equal to the following limit. (m) (부) n 3Ti 37 E cos lim -ㅠ + n n i=1

Q: Determine a region whose area is equal to the given limit. lim 3i 1 + n- co

A: Note: Suppose f(x) is continuous on the interval a,b then ∫abfx dx=limn→∞∑ i=1nfxi∆x where ∆x=b-an…

Q: The lower, upper limit in the evaluation of the area of the region bounded by the two curves 2 y =…

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Q: I – 1 lim 2+1 In r3

A: We have to find the value of limx→1x-1lnx3 using L' Hospital rule.

Q: lim, y0 (1 – 2)" = %3D lim, (Vx3 8x2 - x)% = %3D

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Q: Find the area of the bounded region by the equation y= x+4 , Y - -4 y- ayis and the x-axir.

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Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: Find the limit sin 2z cot 8z lim z cot 4z 2 O 4 O 16 O 1 0 does not exist O O O O O O O O O

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Q: Find the limits in Exercis

A: Given: limy→0sin 3y cot 5yy cot 4y To Find: The value of the given limit

Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

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Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: rea of the region enclosed by

A: we have to find the area of the region bounded by the curve, y=2-x2 .....(1) and the line y=-x

Q: Sketch the region enclosed by the given curves andfind its area. y = x2 ,y = 4x - x2

A: Let us find the point of intersection by equating the two curves  x2=4x-x2 x2+x2-4x=0 2x2-4x=0…

Q: Find the area bound by the curves x = 81 – y² and r = y – 9.

A: We first graph the region using a graphing calculator

Q: Sketch the region enclosed by the given curves. x = 9y?, x = 8 + 7y? y 35 21 30 25 20 5 10 15 20 25…

A: With the help of the graphing utility the area enclosed by the curve of the given equation is shown…

Q: 27. a. Show that the area A, of an n-sided regular polygon in of radius r is a circle sin nr2 2т A,…

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Q: Given that R is the region bounded by the curve y = x+3 and line y= x-3. (b) Describe the region Rby…

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Q: Sketch the region enclosed by the curves x = y² + 2 and x 6 and find its area.

A: Given curve

Q: y = x³ + 2x? – 8x, y = x³ + 5x? -

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Q: Sketch the region enclosed by the given curves andfind its area.   y - cos πx    , y=4x2- 1

A: The given curves are y=cosπx   and  y=4x2-1. Sketch the region enclosed by the above curves as shown…

Q: Sketch the region enclosed by the given curves. y = 3 cos(9x), y = 3 – 3 cos(9x), OSxS1/9

A: Solution is in step 2

Q: Find the area bound by the curves f(z) =- 3a- and g (z) = 3 %3D %3D

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Q: Sketch the region enclosed by the curves y = 2 sin(x), y = 2 csc²(x), x = 7 and x = 4, and compute…

A: The given curves are: y=2 sin x,       y=2csc2x,       x=π4      and      x=3π4

Q: Sketch the region enclosed by the given curves and find its area: y = (x – 3)2, y = x + 3.

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Q: Sketch the region enclosed by the curves y = x2- 4 and y = 3x − 4, and find its area.

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Q: Find the area by the limit definition: [1 ,0) ,"אxy=2x-

A: Limit definition ∫abf(x)dx=limx->∞∑i=1nf(xi)∆xwhere ∆x=b-an and i=1,2,3...n Let xi=a+i∆x ∫012x-x3…

Q: Sketch the region enclosed by the given curves andfind its area.   y = |x| ,    y = x2- 2

A: Given curve  y=x2-2 and y=x When the value of x<0 then, y=-x and and when x>0 then y=0. Solve…

Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit. 2i 1 + lim n-…

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Q: What is the area bounded by the curve y² x – 4 = 0? А. 29/3 В. 30/3 С. 31/3 = x and the line %3D -…

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Q: Sketch the region enclosed by the given curves andfind its area.       y +x = 3     , y = 2  x 2  ,…

A: The given curves are x+y=3 , y=2x2 and y=14x2 , x≥0. To sketch the curve and find the area. The…

Q: Sketch the region enclosed by the curves x − 5 = 4y and x − 21 = (y – 4)², and compute its area. A

A: The given curves are; x-5=4y and x-21=y-42 Now find the point of intersection between the given…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r= 98,0 < 8<…

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Q: Find   Where C is the boundary of the area bounded by the graph y = 3x and y = 4-x2 with a…

A: We know that Green Theorem state: ∫CPdx+Qdy = ∫∫D∂Q∂x-∂P∂ydA

Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit.

A: Here we have to determine the region whose area is equal to the given limit. A=limn→∞ ∑i=1n3n1+3in

Q: Sketch the region enclosed by the given curves andfind its area.   y= 1/4 x2 , y = 2x2 , x + y = 3…

A: Given:                              y=14x2,y=2x2x+y=3;x≥0   Sketching the region and the curves:…

Q: Sketch the region bounded by the graphs of y%3= 1 and y=D4-3x, then find its area.

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Q: Sketch the region enclosed by the given curves andfind its area.       y =|x|     , y =  x2 -2

A: Definition used -      Area between two curves -       If two curves f(x) and g(x) are…

Q: ) Sketch the region enclosed by the given curves and find its area. y = -x² +4x, y=x² – 2x

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Q: Find the limits. Enter "DNE" if the limit does not exist. lim (z,4)→(0,0) 5x2 + 6y cos 4x + 3y + 3…

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Q: Sketch the region enclosed by the given curves andfind its area.    x = 2 y 2  , x =  4 + y 2

A: Definition used -    The area between curves -                        A=∫ab(f(x)-g(x))dx

Q: Evaluate where D is the region bounded by the semicircle x = /4– y² and the y-axis.

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Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: Sketch the region enclosed by the given curves andfind its area. y = 12- x 2   , y = x2 - 6

A: Given curves are y=12-x2y=x2-6

Q: Determine a region whose area is equal to the given limit. Do not evaluate the limit.

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Q: Find the area of shaded region by using Trapezoidal rule YA 2.5 x = y 1.5- 1- y = In 2 0.5- x= e?y…

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Q: Use​ l'Hôpital's Rule to find the limit.   Lim  θ→π/2                3- 3sin theta  / 2+2 cos…

A: Consider the limit

Q: Sketch the region enclosed by the given curves andfind its area.   y =cos x , y= 2- cos x  , 0 ≤ x ≤…

A: Given: The region enclosed by the curves  : y=cos(x)y=2-cos(x)           0≤x≤2π We have to sketch…

Q: Sketch the region enclosed by the given curves. y = 8 cos(x), y = 8 - 8 cos(x), 0<x T

A: This question is related to area bounded by curves, We will use integration to solve it.

Q: (sec 0 – 1) lim 02

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Q: Find the area of the region enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

A: The equation of the curve is:                                            y=x2-2  The equation of the…

Q: Find the limit off as (x.y)-(0,0) or show that the limit does not exist. 2x f(x.y) = x² +x+y? It…

A: Follow next step

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.