In Exercises 9-18, evaluate
C: Smooth curve from (0, 0) to (3, 8).
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Calculus: Early Transcendental Functions
- 8. 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_forwardExercise 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_forwardFind the analytic function f (z)utiv if u = a (1+cose).arrow_forward
- Use the First Fundamental Theorem of Calculus to differentiate the function 5z f(r) = | VI+ t dt.arrow_forwardEvaluate F · dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (2z + 4y) dx + (4x – 3z) dy + (2x – 3y) dz (a) C: line segment from (0, 0, 0) to (1, 1, 1) (b) C: line segment from (0, 0, 0) to (0, 0, 1) to (1, 1, 1) (c) C: line segment from (0, 0, 0) to (1, 0, 0) to (1, 1, 0) to (1, 1, 1)arrow_forwardWhat is the geometrical meaning of an integral of a vector function?arrow_forward
- Use Example 4 to calculate -(r x r'), where r(t) = {t, t2 , et)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
- Is f(z) = z² + 6xy + y² + 2xyi-x + yi analytic nowhere?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_forwardFind the approximation for the Green's function of the one-dimensional acoustic wave equation in the case where velocity is given by: c(x) = aebx , where a and b are real numbers and a > 0. Analyze each case, b 0, in detail.arrow_forward
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