Find the slope of the surface z = 3x/y at the point (5,2,15/2) in the x- and y- directions.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = =…

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Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: The area of the surface obtained by rotating the curve y = 21 x + 1, 0sx< 42 about the x-axis is

A: Given:- y = 21x+1 To find:- Are of rotation about x axis [0, 42]

Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 3y, 1 <…

A: We have to find the surface area of the solid.

Q: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: Find the area of the surface obtained by rotating the curve y=1+4x2 from x=0 to x=6 about the y-axis

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √5 -x, 3 ≤ x…

A: We know that surface area obtained by rotating the curve y=f(x) about x axis between x=a &amp; x=b…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1+5y2,…

A: Recall: Area of the surface rotating about the x-axis: If the curve x=g(y) is given , c≤y≤d , and…

Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: Find the equation of the surface of revolution of x = z2 about the x-axis.

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Q: The area of the surface obtained by rotating the curve y = v64-x2, -2 <x < 2 about the x-axis is

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Q: Find the area of the surface obtained by rotating the curve y = √(5-x),   3≤x≤5 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 = 1/3(y2 +…

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Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 + 2x 1 < x< 1…

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Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0

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Q: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1…

A: Find the exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1+ 2y2 ,1…

Q: Find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 5exy at (3,…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y= square root…

A: The given curve is

Q: Find the area of the surface obtained by rotating the curve y=1+3x² from x = 0 to x = 9 about the…

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Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: Find the area of the surface generated by revolving the curve y =2x-x, 0.5sxs1, about the x-axis.

A: To calculate the area of the surface we use the formula A=2π∫abf(x)1+((f'(x))2 dx

Q: Find the area of the surface generated by revolving the curve: y = V4 -x, -1sxs1 about x-axis.

A: The given curve is: y=4-x2,-1≤x≤1 about x-axis. The formula of surface area=∫ydx

Q: 9. y = x', 0< x< 2

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

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Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

A: The details solution is given below

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.  x=1/3(y2 + 2)…

A: The given curve is,

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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Q: Find the equation of the tangent plane to the surface y = 2x - z at the point (0, -1,-2) y+2z = -5…

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Q: Find the exact area of the surface generated by revolving the curve about the stated axis. y = Vx…

A: The formula for area of surface generated by the revolution of curve y=f(x) , a≤x≤b about x-axis.…

Q: Find the surface area of the portion of the curve x2 = 4y from y = 1 to y =2 when it is revolved…

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Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the…

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