Tuesday, March 24, 2015

Advanced Math Solutions – Limits Calculator, Infinite limits

In the previous post we covered substitution, where the limit is simply the function value at the point. But what if we plug in a value and get a number over 0.  There are some more advanced forms, the indeterminate forms, such as: \frac{0}{0}, \:\:\frac{\infty }{\infty },\:\:\infty -\infty,\:\:\infty \cdot 0,\:\:1^{\infty }, etc. that require more work, but that’s for later.

If evaluating a limit results in the form \frac{1}{0}, then the limit involves an infinite discontinuity. The limit can be determined by analyzing the signs of the factors involved (simply plug in a number from the left and from the right, and check the sign).  Functions of this form will often have different infinite limits from the right and from the left.  When this happens, the two-sided limit does not exist.

Lets start with an example where the limit doesn’t exist, the trick is to show that the limit from the left and the limit from the right at the singularity point are not the same  (click here):



Here’s another example of an infinite limit, pay attention that the even power of the denominator makes both sides of the singularity point approach the same limit  (click here)


One more example of an infinite limit  (click here):



Last example of a limit that diverges (click here):



The more you practice the easier it gets.  Make it a habit, start practicing here.

Cheers,
Michal

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