Fill in the blanks:
`1+x+x^2+x^3+…….`to`infty`=…… for -1< x< 1.

Fill in the blanks: Derivative of x^2 wr.t x^3 is …………… .

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

Fill in the blanks: For x> 0, the function f(x) = log_(1//3) x is a strict _________ function.

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

Fill in the blanks: If f(x) = x^(2//3) , then f'(0) is ……… .

Fill in the blank: (x+b)(x+c)=x^2 + .....+bc.

Fill in the blanks: The function f(x) = x^3 is a strict ________ function.

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

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