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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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The surface S is the portion of the plane z=y+3 that lise inside the cylindrical region x2+y2<=1
(a) Give a unit normal
(b)Sketch the surface S
(c) Compute the surface integral where g(x,y,z(x,y)) = yz
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- a) Compute the equation of the tangent plane to the level surface g(x, y, z) = x'y + 2y°z – 3z*x = 3 Don't round answers unless at the point (1,0, – 1). b) Consider z = z(x, y) as a function of x and y, so z(1,0) = -1. Use the approximation of the surface by its tangent plane to approximate 21 = z(0.99, 0.02). c) Use your approximation of z1 from part b to evaluate g(0.99, 0.02, zı) to five decimal places. Your answer should be close to 3. Is it? the instructions request approximations, or as part of checking your own work.arrow_forwardFind a general expression for a nonzero vector orthogonal to the plane conta r(t)= (a cos t+ b sin t)i+(c cos t+dsin t)j+(e cost+fsin t)k Choose the correct answer below. O A. (b.d.) OB. (a cos t+b sin t,c cos t+d sin t,e cos t+f sin t) O C. (a.c.e) O D. (a+b,c+ d,e + f) DE. (cf-de be- af ad- bc)arrow_forward
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