Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

Q: Use the guidelines of this section to sketch the curve.   y = x/ x-1

A: To find the x-intercept we plug y=0 So x-intercept is 0 To find the x-intercept we plug x=0 So…

Q: Determine the latera recta length of the curve 9x² + 25y² - 225 = 0

A: Solved below

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Find the exact length of the curve.

A:

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

A:

Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

Q: Find the exact length of the curve.

A:

Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D

A: Given: y=x1-x2

Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

A:

Q: 1 - Sketch the curve : y=-(x3– 6x²+9x+6). 6 y=Lcx³-

A:

Q: Find the exact length of the curve. 23/2, Osxs 6

A:

Q: Find the exact length of the curve y3 = 22 from (-1,1) to (8, 4).

A: Use formula of length of curve

Q: y = 4 1 ,2 In x, 1<x < 2 2 -

A:

Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Find the exact length of the curve. 는x - - In(x), 1<x<6 4 2

A:

Q: Find the exact length of the curve. 36y2 = (x² – 4)³, 4 < x < 9,

A:

Q: Find the length of the curve X= -y², 1≤ y ≤9

A:

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

A:

Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

A:

Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

A:

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

A:

Q: Sketch the curve: y² = Xー4

A: A function is an equation that connects the variables x and y. In the xy plane, a function…

Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Find the exact length of the curve. + 4х 1 < x < 3 y

A:

Q: 9y? = 4x3 from the origin to the point (4, %3D 144. Identify the length of the curve

A:

Q: The slope of the curve 2y = ax + b at (1,-1)is -1.Find a, b.

A:

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: 36y2 = (x2 − 4)3,    2 ≤ x ≤ 6,    y ≥ 0

A:

Q: sketch the curve r=1-3costheta

A:

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

A:

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

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Q: Find the exact length of the curve. y = = 0 < x < 6

A:

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

A:

Q: Determine the length of the latus rectum of the curve y² = 8x

A:

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: Find the exact length of the curve. 23/2 12, 0 <x < 1 y =

A: Given : y=23x32,       0⩽x⩽1   To find : Curve length

Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

A:

Q: Find the length of the curve of 8x = y² + 2y-² from y = 1 to y = 2.

A: Length

Q: Find the exact length of the curve. y = 4 글2-글 In(x), 1 < x < 4

A:

Q: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

A:

Q: nsider the curve x3 + y2 - 4xy = -2

A:

Q: Find the exact length of the curve Lou

A: We have to find arc length of curve in required interval .Curve equation is shown below:

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.