## Trending News

Promoted

# Find the Taylor’s series for x^1/2 in powers of x−1.

Find the Taylor’s series for x^1/2 in powers of x−1.

Update:

detail step plx

thx * 7^7

### 1 Answer

Rating

- 魏王將張遼Lv 71 decade agoFavorite Answer
Let f(x) = √x and the n-th derivative can be derived as follows:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywun...

To find the Taylor's series in powers of (x - 1), it is equivalent to solve the Taylor's expansion at x = 1, i.e.

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywun...

Finally, the series expansion, for general terms, can be found as:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywun...

Note: The valid input of x is x >= 0 since the domain of f(x) is non-negative values.

Source(s): My Maths knowledge

Still have questions? Get your answers by asking now.