- #1
irebat
- 7
- 0
use the definition of the derivative to compute the derivative of the function at x=1
f(x) = 1/(1 + x 2) for all x.
i put it into lim[ (f(x)-f(xo))/x-xo ] form and got
[(1/1+x2) - (1/2)] <---------numerator
___________________________ <----- division sign ("over")
x-1 <----------- denomenator
form and from there canceled to
2-1-x2 / 2(x2+1)
and then again to -x2 + 1 / 2(x2+1)
but now I am stuck and can't find a cancellation to calculate the limit at x=1 without getting a 0 in there soemwhere
if i stick this into the limit calculation formula itll just give me a 0 and that's no good. i already know the answer is -1/2 but i can't quite get there. any help is appreciated, thanks.
f(x) = 1/(1 + x 2) for all x.
The Attempt at a Solution
i put it into lim[ (f(x)-f(xo))/x-xo ] form and got
[(1/1+x2) - (1/2)] <---------numerator
___________________________ <----- division sign ("over")
x-1 <----------- denomenator
form and from there canceled to
2-1-x2 / 2(x2+1)
and then again to -x2 + 1 / 2(x2+1)
but now I am stuck and can't find a cancellation to calculate the limit at x=1 without getting a 0 in there soemwhere
if i stick this into the limit calculation formula itll just give me a 0 and that's no good. i already know the answer is -1/2 but i can't quite get there. any help is appreciated, thanks.