is it 0? the numerator becomes as
=
=
=0
The first appearance in print of L’Hˆopital’s Rule was in the book Analyse des Infiniment Petits published by the Marquis de L’Hopital in 1696. This was the first calculus textbook ever published and the example that the Marquis used in that book to illustrate his rule was to find the limit of the function
x =
(√(2a^{3}x−x^{4})) − (a(^{3}√(aax)))
a - (^{4}√(ax^{3}))
as x approaches a, where a > 0. (At that time it was common to write aa instead of a^{2}.) Solve this problem
N.B. : √ = route
oh right i forgot that. i keep think in limit you just ignore the denominator. so you differentiate the numerator and the denominator?
assuming you equation is:
using L'hopital's rule you differentiate both top and bottom? Chain rule?
=
as we get:
=
so
=
=
=
=(4/3)/(3/4)
=16/9
Yes. Then you take the limit. If it exists, it is the same limit as the original expression.
You can always put brackets around them and think of the two terms as a single term. If you don't like to do this for some reason, let be your two terms under the square root sign. Thenim sorry i cant remember how to differentiate the two terms under the square root sign.