Find the exact length of the curve. y? = 16(x + 1)³, 0 0

Q: x Find the length of the curve Y= 6 10x', 1<X<2

A: Given curveY=X56+110X3

Q: Find the exact length of the curve. y = 4 + 2x3/2, 0 < x < 1

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Q: nd the exact length of the curve. y = 3 1. 4x 1sxs2

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Q: r = 3sin(Ɵ) Draw the curve, explaining it down to the smallest detail.

A: Given equation is r=3sinθ We have to draw the curve of r=3sinθ. First of all convert the given polar…

Q: Find the length of the curve x=2t, y=3t, 0≤t≤1

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Q: Find the curve given by x = vt and y =(? – 4), t 2 0 find the slope and concavity at the point (2,…

A: Here, the parametric curve is given by: x=t, y=14t2-4, t≥0

Q: Find the exact length of the curve a 1+ 3t", y = 4+2t", 0 <ts1.

A: Exact answer is 2(2√2 -1)

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

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

Q: 2.x? Sketch the curve y = x? - 1

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Q: Find the exact length of the curve given by 2t2 t3 (0 <t < 5). x = Length = ||

A: Solve for the length of curve

Q: Find the length of the curve. The spiral r= 30 2,0ses

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Q: Find the exact length of the curve. y? = 64(x + 5)3, 0sxs1, y > 0

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Q: Find the length of the curve x y? – 2y, 0< y < 2.

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Q: Find the length of the curve, L. y? = 16 (z+ 3),0sIs1. y > 0

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 7. Y=x³ – 3x? 8. Y= (2x–…

A: 7.)  y = x3 - 3x2 Properties of the curve:   The function takes zero at x= 0 , 3     It has local…

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: y Find the length of the curve x = on 3<y<5. + 18 2y 3.

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Q: Find the length of the curve, L. y = 16 (a + 3)", 0s s1. y> 0

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Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: Find the exact length of the curve.y = 4 + 2x3/2, 0 ≤ x ≤ 1

A: Please see the white board for the formua to calculate the length, L of the curve y = f(x), over the…

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

Q: Determine the slope of the curve y= e^4x at the point x=O? * 1 -4

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Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x 1+2nx b) y = =

A: Get  the asymptote of equation in a: y=limx→∞x2e-x   =0 Thus, plot the graph:

Q: Find the points on the curve as results of the intersection of x² + y? + z? – 2z = 0, y+ z = 1, -…

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: Q5) Find the length of the curve: r = asin? ,0 0.

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Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the lengths of the curves x = (y3/12) + (1/y), 1 ≤ y ≤ 2

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Q: Find the exact length of the curve. 1 + x?)3/2, 0sxs2 y

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Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x³ - 3x? + 4x- 12…

A: y = x3 - 3x2 + 4x - 12y = x2(x -3) + 4(x - 3)y = (x2+4)(x - 3)   X-intercept: (3, 0)    [Real values…

Q: Solve the problem. Find the length of the curve y = In(csc x), 7/4 T/2 VI E

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Q: Find the coordinates of the point/s on the curve y = 2x? which are closest to the point (9,0).

A: We have to find the closet point to the point    (9, 0)

Q: Q4\ Find an equation for the tangent line drawn to the circle (x- 3)2 + (y+ 3)2 = 50 at the point P…

A: Here, the given equation of the circle is (x-3)2+(y+3)2=50. We need to find the equation of the…

Q: 2.x? Sketch the curve y= x² - 1

A: y=2x2x2-1 y=2x2x-1x+1

Q: Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

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Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ? O A. X…

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Q: Find the exact length of the curve. 1 1 s x s 3 y 4x

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

Q: Discuss the properties of the curve and sketch fully: a) y = x2 e-x b) y = 1+lnx

A: To sketch the curve : a) y = x2e-xb) y = 1 + ln xx

Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

Q: Find the exact length of the curve. y ‹ = ²(1 + x²j³/2₁ 3/2, 0≤x≤ 5

A: The objective of the question is determine the length of the given curve.

Q: r= g° ,0<g<\5

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Q: Find the exact length of the curve. y = (2/3)(1 + x2)3⁄2,      0 ≤ x ≤ 2

A: Given: - The curve is, y=23(1+x2)32,  over the interval, 0≤x≤2 To find: - The exact length of the…

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: Find the exact length of the curve. x =  2 3t3,      y = t2 − 2,      0 ≤ t ≤ 2

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Q: d the exact length of the curve. =√y (y - 3), (y - 3), 4 ≤ y ≤ 16

A:

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.