Lateral Surface Area In Exercises 65–-72, find the area ofthe lateral surface (see figure) over the curve C in the x y-plane and under the surface
Lateral surface
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Calculus, Early Transcendentals (Instructor's)
- Dteermine the equation of the tangent plane to the surface given equation G(u, v) = (2u + v, u - 4v, 3u) at the point where: u = 1 and v = 4. %3Darrow_forwardWhat dilation maps triangle ABC onto triangle A'B'C' below? B (x, y) → (2x, 2y) B. (x, y) → (0.5x, 0.5y) 24) C. (x, y) (3x, 3y) D. (x, y) → (-0.5x, -0.5y)arrow_forwardFind the tangent plane at the point (1,-1,1) of the surface f(x,y,z)%3D x^2y+y^2z+z^2x. %3Darrow_forward
- Tangent of x?/3 + y2/3 + z2/3 = a²/3 surface at any point ( xo , Yo ,Zo ) Show that the sum of the squares of the intersecting axes of the plane is constant.arrow_forwardCheck that the point (−1,−1,1) lies on the given surface. Then, viewing the surface as a level surface for a function f(x,y,z) find a vector normal to the surface and an equation for the tangent plane to the surface at (−1,−1,1) x^2−3y^2+z^2=−1arrow_forwardSinx dA where R is the trangle in xy-plane bounded by the x-anise, the line y=x and. the line =arrow_forward
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- Tangent plane 1. Find an equation of the tangent planes to the given surface at the specified point. (a) f(x, y) = 4x² - y² +2y, (-1, 2, 4)arrow_forwardCheck that the point (-2, 2, 4) lies on the surface cos(x + y) = exz+8 (a) View this surface as a level surface for a function f(x, y, z). Find a vector normal to the surface at the point (-2, 2, 4). (b) Find an implicit equation for the tangent plane to the surface at (-2, 2, 4).arrow_forwardA normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane to S at (x, y, 2). a) Find the second intersection point between the normal line to the level surface F(x, y, z) y?- z2 = 1 at the point (1, –1,-1) and the same surface (normal line intersects the level surface at 2 points). x2 +arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage