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1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D.
2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).
The following random sample was selected from a normal distribution: 10, 12, 12, 15, 13, 15 & 16.Test the hypothesis that the true mean exceeds 12. [Use α =.01]
In each of the attached cases show that the set U is linearly independent subset of the vector space V. Give, with justification, a basis of V which contains the set U.
Show that any complex number z with |z| = 1, other than z = 1, can be expressed as with an appropriate choice of the real parameter t.
Let G = UT (n,F) be the set of the upper triangular n x n matrices with entries in a field F with p elements and 1's on the diagonal. The operation in G is matrix multiplication.
Find the equation of horizontal and vertical asymptote of given functions - Find the equations for the horizontal and vertical asymptotes
Application of Calculus-Optimization problem - Show that the shortage length of such a rope occurs when θ 1 = θ 2
Basic probability problems
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
Evaluate the equation of the Straight line - Sketch the curve.Circle: tangent to the line x=3, centre at (5,1)
Suppose that X1=-1, x2=2, x3=4, x4=-3 is a solution of a non-homogeneous linear system Ax = b and that the solution set of the homogeneous system Ax=0 is given by the formulas:
Test the instructor's claim at a five percent level of significance. Write your conclusion?
Fitting of simple linear regression
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