Math Answers

The projection map defined on (R^2,d) where d is the usual metric is continuous.Is it true?

Verify bounded convergence theorem for sequence of function
fn(x)=1/(1+x/n)^n , 0<=x<=1

If the Fourier series of a function f is Cesaro summable,then show that it is Abel summable

Find the measure of following sets
A=Intersection of (a-1/n,b)
E=Q union {1,2,3,4}
E=(5,7) union [7,7.5]

If a Möbius transformation T carries z1 and z2 into a same number w1,then either z1=z2 or else T is a constant map.Is this statement true or false ?why?

Is there any analytic function f exist in a neighbourhood of 0 whose square is z

A field is rectangular and its width is 1/3 as long as its length. What is the area of the field in square yard
s, if the length of the field is 120 yards?

school pep rally,. Randomly drew 36 names out of basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. School is 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. What are the expected frequencies of winners from each class? Expected frequency would be that the freshmen would hold the most prizes (being the largest class) followed by sophomores and Juniors and lastly the seniors as they have a smaller population. b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.
c. What do you conclude?

Find the value of a belongs to real numbers for which ai is a solution of z^4-2z^3+7z^2-4z+10=0 also find all the roots of this equation

Let V be the set of all functions that are twice differentiable in R and S={cosx,sinx,xcosx,xsinx}. a)Check that S is a linearly independent set over R.(Hint: Consider the equation a0cosx+a1sinx+a2xcosx+a3xsinx. Putx=0,π,π 2 ,π 4 ,etc.and solve for ai.) b) Let W=[S]and let T:V→V be the function defined by T(f(x))=d2 dx2(f(x))+2d dx(f(x)). Check that T is a linear transformation on V.