In this unit, we explain what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. We also explain what it means for a function to tend to a real limit as x tends to a given real number. In each case, we give an example of a function that does not tend to a limit at all.

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.

After reading this text, and/or viewing the video tutorial on this topic, you should be able to:

• decide whether a function tends to plus or minus infinity, or to a real limit, as x tends to infinity;
• decide whether a function tends to plus or minus infinity, or to a real limit, as x tends to minus infinity;
• decide whether a function tends to a real limit as x tends to a given real number.

Contents

• The limit of a function as x tends to infinity
• The limit of a function as x tends to minus infinity
• The limit of a function as x tends to a real number

Summary on tutorial Limits of functions

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