# Does #lim_(ararr0^+)(1/a^2)+lim_(brarr0-)(-1/b^2)# diverge?

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I was solving #int_-1^1(1/x^3)dx# and my teacher said it diverges. I was wondering if you can do some kind of cancelling to get #lim_(ararr0^+)(1/a^2)+lim_(brarr0-)(-1/b^2)# equal to zero.

I was solving

##### 1 Answer

Please see below.

#### Explanation:

The standard (basic) definition of convergence of an improper integral tells us that

If

There is another quantity of interest, called the Cauchy Principle Value. For the integral you are working on,

the Cauchy Principle Value is

The standard (or Basic) definition requires us to take the two limit separately. The Cauchy principal value takes the limit of the sum.

As for you specific question, I am not confident about any definition of convergence. that would allow us to answer the question, "Does

I can say that in the extended real numbers this evaluates to