Home
Class 11
MATHS
Expand (1-(x)/(2))^(-(1)/(2)), when |x| ...

Expand `(1-(x)/(2))^(-(1)/(2))`, when `|x| lt 2`.

Text Solution

Verified by Experts

The correct Answer is:
`=1+(x)/(4)+(3x^(2))/(32)+...`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • APPENDIX 2 MATHEMATICAL MODELLING

    NCERT BANGLISH|Exercise EXAMPLE|2 Videos

Similar Questions

Explore conceptually related problems

State whether the following statement is true or false : (d)/(dx)(cos^(-1)x-sin^(-1)x)=(2)/(sqrt(1-x^(2))) , when |x|lt1 .

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

Knowledge Check

  • IF sin ^(-1) ""(x-(x^(2))/(2)+(x^(3))/(4)-(x^(4))/(8)+…….)=(pi)/(6) , when |x|lt 2 then x =

    A
    `2/3`
    B
    `3/2`
    C
    `-(2)/(3)`
    D
    `-(3)/(2)`
  • Similar Questions

    Explore conceptually related problems

    Find (dy)/(dx) in the following : y= sin^(-1) (2x sqrt(1-x^(2))), (-1)/(sqrt(2)) lt x lt (1)/(sqrt(2)) .

    The coefficient of x^(3) in the infinite series expansion of (2)/((1-x)(2-x)) , for |x| lt 1 , is

    3x-2 lt 2x+1

    Find (dy)/(dx) in the following : y= cos^(-1) ((1-x^(2))/(1+x^(2))), 0 lt x lt 1 .

    Find (dy)/(dx) in the following : y= sin^(-1)((1-x^(2))/(1+x^(2))), 0 lt x lt 1 .

    A function is defined as follows : f(x) = {((x^(2))/(2),"when " 0 le x lt 1),(2x^(2) - 3x + (3)/(2),"when " 1 le x le 2):} Discuss the existence of f'(1).

    Find the value of : "tan"1/2["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y^(2))/(1+y^(2))],|x|lt1,ygt0 and xylt1