In Exercise 69 and 70, find curl
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Chapter 15 Solutions
Calculus: Early Transcendental Functions
- Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f (z) = z^3 b) f (z) = 1/z^2arrow_forwardVerify the Sum and Product Rules for derivatives of vector-valued functions.arrow_forwardFind a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 3x2 + y2 and the parabolic cylinder y = 2x2 r(t) = (1,322 + 9^) * Need Help? Read Itarrow_forward
- Let F (x, y, z) = xy² 23 xz5 What is the value of curl F at (3, 2, 1)? (Use syntax like [3,-4,5] for vectors.)arrow_forwardverify green's theorem on both equations ~arrow_forwardFind a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and the cylinder of radius 3 wrapped around the y-axis.arrow_forward
- Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y, z) = x^2+y^2+z^2, (9,2,-8) maximum rate of change direction vectorarrow_forwardWhat is dyldx at the point (1,2) of xy^2 + 2xy = 8 ?"arrow_forwardIntegrate to find F as a function of x and demonstrate the Second Fundamental Theorem of Calculus by differentiating the result from integrating.arrow_forward
- VECTOR DIFFERENTIATION:If A = t(^2)i - tj + (2t+1)k and B = (2t-3) i + j - tk, obtain the following at t=1:a) d/dt(A dot B)b) d/dt(A x B)c) d/dt |A + B| d) d/dt (A x dB/dt)arrow_forwardUse Green’s theorem to compute ∫c F · dr where F(x, y) =<x + 2y, y^2> and C is comprisedof the curve y = x^2, traversed from (0, 0) to (1, 1), followed by the straight line from (1, 1) to (1, 0),followed by the straight line from (1, 0) to (0, 0), all oriented clockwise.arrow_forward(b)Find the derivative of g in the direction of ā = 2i+ curl w at point (0,-1,1): where 8 = In- u + 2 = z(xy+z? } , w = cos -i+ xe*lj+ xyz k U = z W = COS- yzarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage