In Exercises 9-18, evaluate
C: Smooth curve from (0, 0) to (3, 8).
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Calculus: Early Transcendental Functions (MindTap Course List)
- Exercise 1- Determine which of the following functions are analytic: 2 2 d- x²+iy², b = 2xy + i(x²y²) 1 d= (2-1)(2+1) x-iy x²+y2 E- Sinx coshy+icosx sinhy C- )arrow_forward8. Consider the complex function f(z) = x² + y² + 2ixy. a) Show that f'(3i) does not exist. b) Show that f'(3) exists. c) Find f'(3).arrow_forwardFind the analytic function f (z)utiv if u = a (1+cose).arrow_forward
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- What is the geometrical meaning of an integral of a vector function?arrow_forwardPlot the slope field of y = x + y using slopes m = -3, -2,-1,0,1,2. Sketch integral curves for y (0) -6,-4,-2,0, 2. For reference: y = -2x-4+ (y(0)-4)*/2arrow_forwardEvaluate the line integrals using the Fundamental Theorem of Line Integrals: ∫c (yi+xj)*dr Where C is any path from (0,0) to (2,4).arrow_forward
- Let r (t) = The dot product r (1) · r' (1) =arrow_forwardLet F=2(x + y)7+4 sin(y). Find the line integral of around the perimeter of the rectangle with corners (3,0), (3, 6). (-3, 6), (-3,0), traversed in that order. line integralarrow_forwardUse implicit differentiation to find dy/dx in Exercises 1. x2y + xy2 = 6 2. x3 + y3 = 18xy3. 2xy + y2 = x + y 4. x3 - xy + y3 = 1arrow_forward
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