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Use the result of Exercise 31 to evaluate
(a)
(b)
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Chapter 14 Solutions
EBK CALCULUS EARLY TRANSCENDENTALS
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- (1) (16 points) Let f(x, y) = 2x + 3y + In(xy) (a) (6 points) Calculate the gradient field Vf(x, y) and determine all points (x, y) where ▼f(x, y) = (0, 0). (b) (4 points) Calculate the second derivative matrix D²f(x,y).arrow_forwardLet f(x, y) = 2x + 3y+ In(xy)arrow_forward(3) (16 points) Let D = [0, π/2] × [0, 7/6]. Define T: DCR2 R3 by → T(0, 4) = (2 sin cos 0, 2 sin sin 0, 2 cos x). Let S be the surface parametrized by T. (a) (8 points) Determine the normal, call it n(p), for the tangent plane TS at an arbitrary point p = T(0, 4). (b) (4 points) Show that n(p) parallel to the position vector T(0, 4) determined by p? Do the two vectors have the same direction or opposite direction? Explain. (c) (4 points) At which points p, if any, is TS parallel to the xy-plane?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
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