OEF Limit calculus with logarithms or exponentials --- Introduction ---

This module contains 7 exercises about the limit calculus of logarithm and exponential functions. The required and tested skills are: The exercises are composed of several steps. An exercise goes on, even if a false reply has been given at the precedent step. The good answers are provided after each step, to enable further evaluations. NEW EXERCISES. PLEASE SIGNAL ANY BUG...

Limit of u(x)*exp(kx)

We consider the function defined over .
The aim of the exercise is to compute step by step the limits of , at and at respectively.


Limit of u(x)*ln(kx)

Let us consider the function defined over .
The aim of the exercise is to evaluate step by step the limit of , at and at respectively.


Limit of k.ln(ax+b) or k/ln(ax+b)

Let be the function defined over by: .

The aim of the exercise is to evaluate step by step the limit of at .


Limit of k.exp(ax+b) or k/exp(ax+b)

Let be the function defined over by: .

The aim of the exercise is to evaluate step by step the limit of at .


Compared growth : basic properties

The exercise deals with the basic rules of "compared growth" between on one hand logarithms or exponentials of a given variable and on the other hand powers of this variable.


Indeterminate forms with ln or exp

Let be the function defined over by: .

So we have where, for any real in ,   and   .

The aim of the exercise is to evaluate step by step the limit of at .


Basic limits (QUIZZ)

This exercise aims to test the knowledge of basic limits of logarithms and exponentials. Reply as quickly as possible !

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