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(a) g'(zo) #0, then (b) Prove L'Hôpital's rule: If f(z) and g(z) are analytic at zo and f(zo) = g(zo) = 0, but f(z) f'(zo) lim 2+20 g(z) (5) g'(zo) Evaluate the limit: 1+ ez lim z-il+z10 (6) Consider a complex function f(z) = u(x, y) + iv(x, y), z = x+iy, with real and imaginary parts given by u(x, y) = 3x²y², v(x, y) = -6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic.

(a) g'(zo) #0, then (b) Prove L'Hôpital's rule: If f(z) and g(z) are analytic at zo and f(zo) = g(zo) = 0, but f(z) f'(zo) lim 2+20 g(z) (5) g'(zo) Evaluate the limit: 1+ ez lim z-il+z10 (6) Consider a complex function f(z) = u(x, y) + iv(x, y), z = x+iy, with real and imaginary parts given by u(x, y) = 3x²y², v(x, y) = -6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) g'(zo) #0, then (b) Prove L'Hôpital's rule: If f(z) and g(z) are analytic at zo and f(zo) = g(zo) = 0, but f(z) f'(zo) g'(zo) (a) (b) Evaluate the limit: = Consider a complex function f(z) = given by lim zzo g(z) 1+ eπz lim z→il+210 (6) u(x, y) +iv(x, y), z = x+iy, with real and imaginary parts 22 u(x, y) = 3x²y², v(x, y) = −6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic. (7)
Transcribed Image Text:(a) g'(zo) #0, then (b) Prove L'Hôpital's rule: If f(z) and g(z) are analytic at zo and f(zo) = g(zo) = 0, but f(z) f'(zo) g'(zo) (a) (b) Evaluate the limit: = Consider a complex function f(z) = given by lim zzo g(z) 1+ eπz lim z→il+210 (6) u(x, y) +iv(x, y), z = x+iy, with real and imaginary parts 22 u(x, y) = 3x²y², v(x, y) = −6x²y². Determine where this function is differentiable with respect to z. Determine where this function is analytic. (7)
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