Take 10 minutes to prepare this exercise.
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A detailed solution is then proposed to you.
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Question
Find the following limits:
a)
b)
c)
a) Divide the numerator and the denominator by
b) Multiply the numerator and the denominator by
c) Apply the calculation rules on the limits, this is not an indeterminated form.
a) We have an indeterminated form
we know that
converges towards
when
goes to
it is a limit to know, hence
goes towards
when
goes to
We can also use a more generic result: the limit of a quotient of two polynomials is equal to the limit of the quotient of the terms of higher degree.
b) We have an indeterminated form
We multiply it by the “conjugated expression” :
The denominator is the sum of two functions going to
when
goes to
hence it goes to
and the inverse goes towards
c) When
goes towards
goes towards
and
goes towards
by positive values, hence the quotient goes to