Fill in the blanks:
`1+2x+3x^2+4x^3+`………..to `infty`=….. For -1`ltxlt`1.

Fill in the blanks : d/dx |3x +4| = ______

Fill in the blanks : int(2dx)/(1-cos2x) =……………… .

Fill in the blanks : d/dx [sin^-1 *(2x)/(x^2 +1)] =________

Fill in the blank: If f (X) = 4-(x-7)^3 , then f^-1 (x) = ______

Fill in the blanks: The curves y = 4x^2 + 2x - 8 and y = x^3 - x + 10 touch each other at the point..........

Fill in the blanks: If y = 2 tan^-1 x + sin^-1 ((2x)/(1+x^2)) for all x, then ………… le y le …….

The sum of the series 1+3x+6x^2+10x^3+………….infty is:

Fill in the blanks: For x in R, tan^-1 (x^2 +1) + cot^-1 (x^2 +1) is equal to ……………..

Fill in the blanks: For |x| ge sqrt2, sec^-1 sqrt(x^2 -1) + cosec^-1 sqrt(x^2-1) is equal to ……………

Fill in the blanks: If cos(tan^-1 x + cot^-1 sqrt3) = 0 , then value of x is ………