Analysis Basics

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel to ask then on the forum.

Question

Find the following limits:

a)

b)

c)

Indice

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.

Solution

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

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