Am using Spivak and he defines limit of a function f(adsbygoogle = window.adsbygoogle || []).push({});

1. As it approaches a point a.

2.As it approaches infinity.

He also defines limit f(x)=∞

x->a

But though in solving exercises, we can see that all the three definitions are consistent with each other, I am not satisfied by the arguement that these specially defined limits follow all the property like;

Let lim f(x)=m and lim g(x)=n, then to prove lim f(x)*g(x)= m*n...

x->∞ x->∞ x->∞

Let lim f(x)=m here m is not equal to 0, then to prove lim ( 1/f(x))=(1/m)

x->∞ x→∞

In some calculus(like Kuratowski) and analysis books, I could see that they first talk about series, convergence, divergence and so on....Then they talk about epsilon-delta definition of limit and show that this definition is consistent with the one obtained through sequence and series. So, is learning sequences and series(and some concepts like bounded sequence) necessary for proving such and such theorems?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Proving limit theorems when limit tends to infinity

Tags:

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Proving limit theorems |
---|

I A rigorous definition of a limit and advanced calculus |

I Proving the Linear Transformation definition |

B Question about a limit definition |

I Looking for additional material about limits and distributions |

I A problematic limit to prove |

**Physics Forums | Science Articles, Homework Help, Discussion**