For a complex variable Ƶ, if \(f\left( Ƶ \right) = \left\{ {\begin{ – McqOptions

MCQOPTIONS

1.	For a complex variable Ƶ, if \(f\left( Ƶ \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{ Ƶ}{{\left\| Ƶ \right\|}}}&{for\;Ƶ \ne 0}\\ {0,}&{for\;Ƶ = 0} \end{array}} \right\}\) then,
A.	\(\mathop {\lim }\limits_{Ƶ \to \infty } f(Ƶ) = 1\)
B.	f(Ƶ) is discontinuous at origin
C.	f(Ƶ) is continuous at origin
D.	\(\mathop {\lim }\limits_{Ƶ \to \infty } f(Ƶ) = i\)
Answer» C. f(Ƶ) is continuous at origin

Discussion

No Comment Found

Related MCQs

Polar form of the Cauchy-Riemann equations is
If f(z) = (x2 + ay2) + i bxy is a complex analytic function of z = x + iy, where \(i = \sqrt { - 1} \), then
Assuming \(i = \sqrt { - 1} \) and t is a real number, \(\mathop \smallint \limits_0^{\frac{\pi}{3}} {e^{it}}dt\) is:
\(1\;+\;\frac{x^2}{2!}\;+\;\frac{x^4}{4!}\;+\;\frac{x^6}{6!}\;+\;.....\) stands for.
If f(z) is an analytic function whose real part is constant then f(z) is
Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integral \(\displaystyle\oint_C \dfrac{dz}{z^2 (z-4)}\) is
If then the value of xx is
In the neighbourhood of z = 1, the function f(z) has a power series expansion of the form
An analytic function of a complex variable z = x + iy is expressed as f (z) = u(x,y) + iv (x, y) where i = √-1 . If u = xy, the expression for v should be
If C is a circle of radius r with center z0, in the complex z-plane and if n is a non-zero integer, then \(\mathop \oint \nolimits_C \frac{{dz}}{{{{\left( {z - {z_0}} \right)}^{n + 1}}}}\) equals