abstract algebra, Mathematics

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What is the integratin of 1/sin2x?, ∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cos...

∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x

Computing limits , Computing Limits :In the earlier section we saw that t...

Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi

PROBABILITY, Find the probability of drawing a diamond card in each of the ...

Find the probability of drawing a diamond card in each of the consecutive draws from a well shuffled pack of cards,if the card drawn is not replaced after the first draw.

Determinant, The subsequent topic that we require to take a look at is the ...

The subsequent topic that we require to take a look at is the determinant of a matrix. The determinant is in fact a function that gets a square matrix and converts this in a number

Find the derivatives, Find the derivatives of the following functions a)...

Find the derivatives of the following functions a)      y = 5x 4 +3x -1-x 3 b)      y = (x+1) -1/2 c)      y= e x2+1 d)     y= e 3x lnx e)     y =ln(x+1/x)y

Economics, A mortgage lender seeks to maximize the expected value of its po...

A mortgage lender seeks to maximize the expected value of its portfolio. The portfolio, of course, is the sum of all of the mortgages in it, so no generality is lost by examining t

Percent problems.., I have a graph, i need to determine the many hours per ...

I have a graph, i need to determine the many hours per day becky spends on math activity if she does it 25% of her day.

Equivalence class and equivalence relation, 1. For a function f : Z → Z, le...

1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc

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