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1. Verify whether the function f(2) = e=Y sin x – ie- cos x is entire or not. 2. Show that the function f(2) = xy + iy is nowhere analytic.

1. Verify whether the function f(2) = e=Y sin x – ie- cos x is entire or not. 2. Show that the function f(2) = xy + iy is nowhere analytic.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 44E
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1. Verify whether the function f(z) = e-Y sin x – ie- cos x is entire or not. 2. Show that the function f (2) = xy + iy is nowhere analytic.

1. Verify whether the function f(z) = e-Y sin x – ie- cos x is entire or not. %3D 2. Show that the function f (z) = xy + iy is nowhere analytic. 3. Show that u(x, y) = 2x – x3 + 3xy² is harmonic. 4. Find the harmonic conjugate of u where u(x, y) = x² – y? – 2xy – 2x + 3y. - - - = sinh 4x cos 4y + i cosh 4x sin 4y satisfies 5. Verify whether the function f(z) Cauchy-Riemann equations or not.
Transcribed Image Text:1. Verify whether the function f(z) = e-Y sin x – ie- cos x is entire or not. %3D 2. Show that the function f (z) = xy + iy is nowhere analytic. 3. Show that u(x, y) = 2x – x3 + 3xy² is harmonic. 4. Find the harmonic conjugate of u where u(x, y) = x² – y? – 2xy – 2x + 3y. - - - = sinh 4x cos 4y + i cosh 4x sin 4y satisfies 5. Verify whether the function f(z) Cauchy-Riemann equations or not.
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