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This limit leads to the indeterminate form so we can apply the l’Hôpital’s
rule.
.
Indeterminate form .
.
Indeterminate form .
with
This limit leads to the Indeterminate form . The derivative of the numerator is , and
the derivative of the denominator is .
Calculate the following limits.
This limit leads to the indeterminate form . But you can rewrite the limit
as:
and that leads to the indeterminate form , so that we can apply l’Hopital’s rule. The
ratio of the derivatives is
The limit of this expression for to infinity is still the indeterminate
form . So we apply l’Hôpital’s rule again, and finally find
This limit leads to the indeterminate form , to which l’Hopital’s rule can not be
directly applied. But you can rewrite the limit as:
and that leads to the indeterminate form , so that we can apply l’Hôpital’s rule.
This limit leads to the indeterminate form , to which l’Hopital’s rule can not be
directly applied. But you can rewrite the limit as:
and that leads to the indeterminate form , so that we can apply l’Hôpital’s rule.
This limit leads to the indeterminate form . We use the identity for the
calculation.
We have applied l’Hôpital’s rule 4 times. Check that l’Hôpital’s rule was applied each
time with the indeterminate form .
We cannot use the rule that the limit of a difference is the difference of the limits
because this will result in the indeterminate form . However, we can put the
fractions on the common denominator and get the indeterminate form , so that
l’Hôpital’s rule can be applied. We will use the identity for the calculation.
Only after the fourth time, we do not encounter an indeterminate form. Check
that the l’Hôpital’s rule was applied each time for the indeterminate form .
We cannot use the rule that the limit of a difference is the difference of the limits, because
this will result in the indeterminate form . However, we can put the fractions on a common
denominators and get the indeterminate form , so that l’Hôpital’s rule can be applied.
Check that l’Hôpital’s rule was applied in each case for the indeterminate form .
2023-06-23 10:16:53
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
Basic Math Course