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 TRANSCENDENTAL FUNCTIONS
- 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_forwardR(a, b) = (2b + cosa, 2a + sin b, ab) Determine the equations for the (a) tangent plane and (b) the normal line to the surface S at the point (-1,2TT, 0)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_forward
- Find the tangent plane at the point (1,-1,1) of the surface f(x,y,z)%3D x^2y+y^2z+z^2x. %3Darrow_forwardSinx dA where R is the trangle in xy-plane bounded by the x-anise, the line y=x and. the line =arrow_forwardConsider the function f(x,y)=|x|+|y| Sketch the surface z = f(x,y) Draw the level curves of the functionarrow_forward
- derivative 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_forwardQI/ Find the tangent plane of the function f(x, y) = e**+y* at (0,0). Is it parallel to the plane 2x + 3y- z 1 or not? Why?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). -4i + 4k (b) Find an implicit equation for the tangent plane to the surface at (-2, 2, 4). X-Z +6=0arrow_forward
- 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_forwardParameterize the intersection of the cone z = x2 + y2 and the plane z = 2x + 4y + 20. Find the tangent line at the point (4, -2, 20).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage