1+(1+a)x +(1+a+a?)x2 +....0 lta,xlt1equals

1+(1+a)x+(1+a+a^2)x^2 +.......... 0lta,xlt1 equals (1) 1/((1-x)(1-a)) (2) 1/((1-a)(1-ax)) (3) 1/((1-x)(1-ax) (4) 1/((1-x)(1+a))

Differentiate cos^(-1)((1-x^2)/(1+x^2)) , 0lt xlt1 with respect to x

Let f(x)=[|x|-|x-1|]^(2) What is f'(x) equal to when 0lt xlt1 ?

If 0ltalt1 , prove that 0lta^2ltalt1

If x^(4)+x^(-4)=2599 , then one of the values of x-x^(-1) , where xlt0 is equal to:

if f(x) ={{:( x-1, xlt 0),( x^(2) - 2x , x ge 0):} , then

Let f(x)={x/2-1,0lt=xlt=1 1/2,1lt=xlt=2}g(x)=(2x+1)(x-k)+3,0<=x<=oo then g(f(x)) is continuous at x=1 if k equal to:

If xlt0 , then value of tan^(-1)(x)+tan^(-1)(1/x) is equal to