Does anybody know how to solve the limit of #(x^x-x^{x^2})/(1-x)^2# when #x->1# ?
1 Answer
-1
warning: long answer
Explanation:
plugging
since this is indeterminate form, you can find the derivative of the numerator and divide that by the derivative of the denominator and still have the same limit (L'hopital's rule)
limit is now:
[SIDE NOTE: to find the derivatives of
then use implicit differentiation:
substitute y back in:
do the same for
the limit simplifies to:
plugging in
limit becomes:
(might want to check https://www.derivative-calculator.net/)
plugging in
check with this graph:
graph{(x^x-x^(x^2))/((1-x)^2) [-2.605, 6.165, -2.768, 1.617]}