Lateral Surface Area In Exercises 43 and44, find the area of the lateral surface over the curve C in the xy-plane and under the surface
Lateral surface area =
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EBK CALCULUS: EARLY TRANSCENDENTAL FUNC
- What 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_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_forwardDteermine 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_forward
- Sinx dA where R is the trangle in xy-plane bounded by the x-anise, the line y=x and. the line =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_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). -4i + 4k (b) Find an implicit equation for the tangent plane to the surface at (-2, 2, 4). X-Z +6=0arrow_forward
- Check 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_forwardderivative Q3: For the surface f(x, y, z)= In (xyz), find: (1) the gradient of f at (1,1,2), (2) the directional at (1,1,2) in the direction of i=i+2j-2k; (3) the max. and min directional derivative and their (4) the parametric equation of the tangent plane and the normal line to the surface at (1,1,2). directions;arrow_forward
- True False The equation of tangent plane to the surface f(x,y, z) = x² +y +z-9= 0 is x+y+z= 14. at the point (1,2,4) True Falsearrow_forwardTangent to the curve x +y 2x at the points (1,1) and (-1,1) are a) paralel c) Intersecting but not at right angles e) None of them b) perpendicular d) Skewarrow_forwardCheck that the point (1,-1,2) 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,-1,2). vector normal = tangent plane: 4x² - y² +3z² = 15arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage