Find the curve lenght from t=o to te2T of the given curve C: P(E) = (cos3t) î + (sin 3t) Î t ? tJE e + 2

Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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Q: find an equation y = f (x)for the parametric curve and compute dy/dx in two ways: using Eq. (8) and…

A: Consider the parametric curve Ct=2t+1 , 1-9t Since, x , y=2t+1 , 1-9t⇒x=2t+1 , y=1-9t Or,…

Q: Evaluate the arc length of the curve generated by the parametric equations below for t (-1,1) x(t)=…

A: The expression for the arc length of the parametric curve is; L=∫abx't2+y't2dt   Given: xt=3+3t2 ;…

Q: Find of the curve the curve lenght from t=o to t=2M given C: P(t) = (cos 3t) î + (sin 3t) Î + ? tVt…

A: Here I am attaching image so that you understand each and every step.

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

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Q: Sketch the path using the following parametric equations x(t) = 3t – 7 and y(t) = 4 sin t+1 0st55,…

A: Here we need to find different points for different values of t

Q: Find the length of the curve C defined parametrically by C: 2(t) = e'cost, v(t) = e'sint, 0SISR…

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Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

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

Q: Consider the plane curve given by the parametric equations x = t² + 3t - 26 y = t² + 3t - 28 - What…

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Q: Find f F. dr for F = 2yi – (sin y)j on the curve counterclockwise around the unit circle C starting…

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Q: Find the arclength of the curve r(t) = (6t2, 2v6 t, In t) , for 1SI58. L =

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Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: Let x = 9t?, y = 7t° – 8t?. d²y as a function of t, then find the concavity to the parametric curve…

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Q: Find the lengths of the curves r(t) = (2 cos t)i + (2 sin t)j + t2k, 0 ≤ t ≤ π&gt;4

A: Given r(t)=2costi+2sintj+2tk We need to find the length of the curvature . The length of the curve…

Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: •x= 5+4 sin 0 and y = -3 + 2 cos 0

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Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. (a). Find the…

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Q: Consider the parametric curve given by x = t2 + 5, y= e* est + 2t. 3t Find the slope of the tangent…

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Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

Q: Find the arclength of the curve r(t) = (2 sin t, 6t, 2 cos t), –7 < t < 7

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Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find for the parametric curve c(t) = (41°, 2r² – 8) at the point t = 2. (Use symbolic notation and…

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Q: consider the parametric curve x=t2 , y=9t-t3 . find dy/dx at t=2.

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

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Q: What is the slope at t = −2 ?

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Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: A curve C is defined by the parametric equations x(t) = 3 + t“ and y(t) = t° + 5t.Which of the…

A: Given,         A curve C is defined by the parametric equations xt=3+t2 and yt=t3+5t.

Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

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Q: Find the length of the curve C defined parametrically by C: r(t) = e' cos t, y(t) = e sin t, 0<t< T

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Q: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

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Q: Find the length of the following three-dimensional curve. r(t)= (sin t, cos t, 2t), for 0sts4

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Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: Find the length of the following​ three-dimensional curve. r(t)=cos t, sin t, 3t​, for 0≤t≤2

A: Given that rt =cost,sint,3t  for 0≤t≤2 find the length

Q: Find the length of the curve C defined parametrically by C: r(t) = y(t) = e' sin t, 0<t<n e cost,…

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Q: Find T(t) and a set of parametric equations for the tangent line to the helix given by 7(t) = 2…

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Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…

Q: A curve is defined by the parametric equations: x(t) = e' cost, y(t) = e' sint dy d²y Determine and…

A: The tangent line to the curve in parametric form is given as follows

Q: Find the speed of the curve F(t) = (4cos (t), 4 sin(t), 6t) at t = 3 %3| Speed =

A: Consider the curve  r(t)=&lt;4cost2,4sint2,6t&gt;

Q: Find the length of the curve C defined parametrically by C:x(t) = e' cos t, y(t) = e' sint, 0<tS#…

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Q: Let C be the part of the curve x? + y² = 1 with y 2 0, oriented counter- clockwise. Evaluate F. dr,…

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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.