find limx→a (x^n-a^n)/(x^m-a^m)
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Step-by-step explanation:
lim
x
n
−a
n
x
m
−a
m
is of the indeterminate form
0
0
So, we can apply L'Hospital rule.
dx
d
(x
m
−a
m
)=mx
m−1
−0
=mx
−m−1
dx
d
(x
n
−a
n
)=nx
n−1
−0=nx
n−1
x→a
lim
x
n
−a
n
x
m
−a
m
=
x→a
lim
dx
d
(x
n
−a
n
)
dx
d
(x
m
−a
m
)
=
nx
n−1
mx
m−1
=
n
m
x
m−n
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