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These are questions asked by Lonely


please help me here:

i have

p(n):= (2310*n^5+5775*n^4+5019*n^3+(3507/2)*n^2+(409/2)*n+5/2)/(27720*n^7+97020*n^6+132300*n^5+88200*n^4+29400*n^3+4410*n^2+210*n)

how can apprximate p(n) with another polynomial (say: a second degree polynomial in n) or a rational function (ration of two second order polynomials) of less degree of n? and how good is that approximation

thanks in advance


please help me here:

I have:


now i want to multiply by (n+1/2) that is


now i want to express it in a simples form. may be like this:

c(n) + d(n)/p(n)





How can i find:


int(x*sinh(x)/sqrt(1-sinh(x)*sinh(x)), x = 0 .. log(sqrt(2)+1))


int(x*sinh(x)/sqrt(1-sinh(x)^2), x = 0 .. ln(sqrt(2)+1))


with maple

Please help me finding a formula for nth derivative of

1/sqrt(1-x^2) and 1/sqrt(1+x^2)

Please help me how can i find nth derivative of


when i do

diff(1/(1+x*x), `$`(x, n))

maple gives

diff(1/(1+x^2), `$`(x, n))

even if i do


maple still gives the same answer.


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