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5. Show that the function f(z) = (x, 0) has the value 1 at all nonzero points on the real and imaginary axes, where z = and z = (0, y), respectively, but that it has the value -1 at all nonzero points on the line y = x, where z = (x,x). Thus show that the limit of ƒ(z) as z tends to 0 does 2

5. Show that the function f(z) = (x, 0) has the value 1 at all nonzero points on the real and imaginary axes, where z = and z = (0, y), respectively, but that it has the value -1 at all nonzero points on the line y = x, where z = (x,x). Thus show that the limit of ƒ(z) as z tends to 0 does 2

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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5. Show that the function f(z) = = (x, 0) has the value 1 at all nonzero points on the real and imaginary axes, where z = (0, y), respectively, but that it has the value -1 at all nonzero points on the line y = x, where z = (x,x). Thus show that the limit of f(z) as z tends to 0 does and z = *See for inctor
Transcribed Image Text:5. Show that the function f(z) = = (x, 0) has the value 1 at all nonzero points on the real and imaginary axes, where z = (0, y), respectively, but that it has the value -1 at all nonzero points on the line y = x, where z = (x,x). Thus show that the limit of f(z) as z tends to 0 does and z = *See for inctor
SEC. 19 DERIVATIVES 55 not exist. [Note that it is not sufficient to simply consider nonzero points z = (x, 0) and z = (0, y), as it was in Example 2, Sec. 15.] nt (8) in Theorem 2 of Sec. 16 using
Transcribed Image Text:SEC. 19 DERIVATIVES 55 not exist. [Note that it is not sufficient to simply consider nonzero points z = (x, 0) and z = (0, y), as it was in Example 2, Sec. 15.] nt (8) in Theorem 2 of Sec. 16 using
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