9.40. Show that the 0-parameter curves on the surface x = (r cos 0)e¡ + (r sin 0)eg + f(0)eg are parallel.

Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

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Q: 24. Evaluate | x/x² + y² dA, where D is the shaded region enclosed by the lemniscate curve r² = sin…

A: Consider the given:

Q: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

Q: 1(b) Find the surface area generated by revolving the portion of the curve y x2 + 1 between x=0 and…

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Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

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Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

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Q: 16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: To compute the surface area of the surface obtained by revolving the given curve about the axis x =…

Q: take the fequan bunded by Hhe Seguen Curve fla).2+ Sinlx) the x atis 3R and X= Vz X:0 and fond the…

A: We will find out the required value.

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: 5) Evaluate the integral (e* - y) dx + (sin y + x)dy using Green's theorem where Cis bounded by y =…

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Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

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Q: 5) Determine the area of the surface obtained by rotating the arc y = Vx –1 around the x- axis from…

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Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…

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Q: (10) Find the work done by F = -yi+ xj+ zk on a particle moving along the helix r(t) = where 0 < t <…

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Q: 4. Find the radius and centre of curvature of the curve x = (1 - at) cos t + a sin t, y = (1 – at)…

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Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

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Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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Q: 1 Consider the curve defined by the parametric equations x = ÷ť & y=÷ť for 2<t<3 2 3 Determine the…

A: take derivative

Q: 3. Find the surface area generated by revolving the curve y = 2+ cos 0, x = sin 0 ; 0 <O< 2n about…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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Q: 3 4. Find the arc length of the graph of the function f(x) =;(x² + 1)ī over the interval [0, 1]. =…

A: y =f(x) =23(x2+1)32f(x)=23(x2+1)32f'(x)=23*32(x2+1)12(2x)f'(x)=(2x)(x2+1)12 The Formula for arc…

Q: 6. Consider the same curve from the last problem, C parametrized by T(t) = (2 cos t, –1,2 sin t)…

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Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

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Q: 3. Find the exact area of the surface resulting from rotating y = v1 + e* from x = 0 to x = 1 about…

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Q: Consider the following. x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 8? Set up an integral that…

A: Our objective is to setup thr integral

Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: 1(a) Find the arc length of the curve 2x = 3y2/3 over the interval from y=0 to y=1  1(b) Find the…

A: (a) The arc length of the curve 2x=3y23 over the interval y=0 to y=1 can be calculated by using…

Q: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find the maximum, minimum and inflection points of the fur y= 3 sin 2x at [0, T].

A: Solution:-

Q: у 3 1 + sin х, 0 <x< т/2 y

A: The given curve is y=1+sinx and the limit is 0≤x≤π2 The Surface area is given by S=∫x2πy1+y'2dx or…

Q: #4

A: Find the tangent plane to the given surface at the specified point

Q: The area of the surface generated by rotating the curve y = 2 + e*, where 1 < x < 2, about the…

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = cos -х 0< x…

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Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

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Q: Find the area of the surface generated when the given curve is revolved about the given axis 1 = (e…

A: Given y=112e6x+e-6x  ,for -2≤x≤2  Area of surface of curve when revolved about x-axis…

Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: The integral that represents the length of the curve 7(t) = (t, cos (2t312), sin (2t312)), where Ost…

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Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where…

A: Given curve is, r→(t)=&lt;2t, cos(2t32), sin(2t32)&gt;, t∈[0,1] Now,…

Q: 1. (a) Find the exact area of the surface obtained by rotating the curve y = e* about the x-axis…

A: