Q: the surface area of the surface generated by revolving the curve c(t) = (t, sin(t)) about the x-axis…
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Q: Find the exact value of 0.049768 x³y²z ds, where C is the curve with parametric equations x = e¯t…
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Q: 7. Identify the surface for each of the following equations. (a) z = r² (b) r² + z² = rl (c) p = 4…
A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: (4) Find the surface area of the cone S a) b) c) d) 7-√√2 5-√3 p(r, 0)=(r cos 0,r sin 0,r) for 0≤0…
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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…
A: Find the derivatives with respect to θ
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A: y = x2 - 4 (a) we choose x, θ as perameter = (x, - (x2 + 4) cos θ, -(x2 +4) sin θ) (b) dr→dx= (1,…
Q: 7. Identify the surface for each of the following equations. (a) z = r? (b) r² + z² = r' (c) p= 4…
A: We to identify the surface for each of the following equations a z = r2 consider x = r cosθ, y…
Q: 1. Find an equation for the tangent plane to the surface x cos z + yře*z =4 at Po(3, –1, 0)
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Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…
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Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…
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Q: 5. Given that r(t) = 3i + e* sin tj + e cos tk Find equations of the normal plane and osculation…
A: We have to find equation of normal and oscillating plane of above curve.
Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,
A: From the given problem : rt=eti+etsin2tj+etcos2tk So, x=et, y=etsin2t , z=etcos2t . As we…
Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…
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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = ,…
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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: U SIII u' cos u?, EXAMPLE 6.6.3 For a surface of revolution defined by x u! oin o? COS 3 flol) aub…
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Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…
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Q: The circle of radius 3 centered at the origin Ex. to calculate the area of the given region.
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Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the…
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Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…
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Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…
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Q: s) The given curve is rotated about the x-axis. Find the are √2x +3,0 ≤ x ≤ 6. of the resulting…
A: Introduction: The formula for the surface of revolution of the curve is given by,…
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Q: .... ........ 4.8. Find the area of the surface generated by revolving the curve x = cost, y =…
A: See the details solution in below
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: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.
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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. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…
A: Recall: sin2t+cos2t=1
Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…
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Q: B. Find the length of the circle of radius r defined parametrically by x = r(v1 – sin t) and y =…
A: We need to find the length of the circle which is parametrically defined as below.
Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1
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Q: Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y =…
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Q: Consider the curve y = 3 sin(2x), where 0 < x < n/2. Find the surface area when this curve is…
A: We have given the function; We know the formula for surface area by revolution;
Q: 5. Consider the two curves r= / cos(0) and r= V2 cos(0), -T/2<0ST/2,whose polar plo 0.6 0.4 0.2 0.2…
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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: #4
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Q: Find the area of the surface obtained by rotating the given curve about the x-axis. x=…
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Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.
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Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…
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Q: 3) Find the area of the surface that results from rotating the curve Y = sin X, 0<X< 1 about the X…
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Q: Consider the curve y = 3 sin(2x), where 0 < x < T/2. Find the surface area when this curve is…
A: To find the surface area when the curve the is rotated about the x-axis.
Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…
A: Find the surface area rotating the curve about x axis
Q: 1. (a) Find the exact area of the surface obtained by rotating the curve y = e* about the x-axis…
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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 4y2, 1 s…
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- 30. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem using lagrange9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. (a) about the x-axis (b) about x = 4 please answer both a and b 1 to t to 2 x=4t, y=sqrt(t^2) but if you can only do one please do b
- The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution,Find the integral surface through the curve y: 2x = y^2 + z^2, y + 1 = 0Consider the surface x^4+ 3xz + z^2+ cos( πxy ) = -2 and the point P0 ( -1, 1, 2) on that surface. Find an equation of (a) the tangent plane at P0 (b) the normal line to the surface at P0Find a generating curve and the axis of revolution for the surface x2 + 3y2 + z2 = 9.
- given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane rotating through the y-axisFind an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2, (1,-1,1)