limx→0 c^x-1/x is equal to
Answers
Answer:
Explanation:Formula
lim
x
→
0
a
x
−
1
x
=
log
e
a
Introduction
If
a
is a constant and
x
is a variable, then quotient of subtraction one from
a
raised to the power of
x
by
x
is written as
a
x
−
1
x
and the limit of this special exponential function is written mathematically as follows.
lim
x
→
0
a
x
−
1
x
The limit of this special exponential function is equal to natural logarithm of
a
. It’s used as a formula in finding the limits of exponential functions in calculus.
Other forms
This standard result in limits can be written in several ways in calculus.
(
1
)
lim
y
→
0
c
y
−
1
y
=
ln
(
c
)
(
2
)
lim
u
→
0
m
u
−
1
u
=
ln
(
m
)
Proof
Let’s prove the limit of quotient of difference of
a
x
and
1
by
x
as
x
approaches
0
is equal to natural logarithm of
a
.