" 20."(1)/(x(x^(4)-1))

Evaluate the following limits : lim_(x rarr 1) (x^(1/20)-1)/(x^(1/40)-1)

If x+sqrt(x^(2)-1)+(1)/(x+sqrt(x^(2)+1))=20 then x^(2)+sqrt(x^(4)-1)+(1)/(x^(2)+sqrt(x^(4)-1))=

int (1)/(4x^(2)-20x+17)dx

lim_(x rarr oo) ((x+2)^(10)+(x+4)^(10)+...+(x+20)^(10))/(x^(10)+1)= ______.

(20)/((x-3)(x-4))+(10)/(x-4)+1>0

lim_ (x rarr oo) ((x + 2) ^ (10) + (x + 4) ^ (10) ++ (x + 20) ^ (10)) / (x ^ (10) +1) =

If f(x) =tan^(-1)((x)/(1+20x^(2))) , show that, f'(x)=(5)/(1+25x^(2))-(4)/(1+16x^(2))

Find the minimum value of log_(x_(1))(x_(2)-(1)/(4))+log_(x_(2))(x_(3)-(1)/(4))+......+log_(x_(20))(x_(1)-(1)/(4)) over all x_(1),x_(2),...x_(20)in((1)/(4),1)

If (1-2x+x^(4))^(5)=a_(o)+a_(1)+a_(2)x^(2)+......a_(20)x^(20) then a_(0)+a_(1)+a_(2)+......a_(20) is

If 64x^(2) + (1)/(64 x^(2)) = 20 , then 8x - (1)/(4x) can be "_______"