Determinate using L'Hopital.
Answers
Answer:
Example5.30. Undefined because it Leads to Contradiction.Suppose that
f
(
x
)
=
1
x
.
What happens when
x
=
0
?
Then
f
(
0
)
=
1
/
0
,
but
1
/
0
is undefined. Why is that? Let's assume this value is defined. This means that
1
/
0
is equal to some number, call it
n
.
Then
1
0
=
n
1
÷
0
=
n
1
=
n
×
0
1
=
0
Clearly, 1 is not equal to 0, and so this statement is a contradiction. In fact, if we analyze the satament
1
=
n
×
0
,
we notice that there is no number for
n
that will satisfy this equation. Therefore,
1
/
0
could not have been a number, and hence we say
1
/
0
is undefined. This is the reason why we write that the domain of
f
is given by
Answer:
So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.