Other Indeterminant Forms

I.  Quiz

II.  Homework

III.  Hidden Forms of L'Hopital's Rule

We can also use L'Hopital's rule when we have expressions of the form (0)(infinity), (infinity)⁰, and infinity - infinity

Example:  (0)(infinity) 

Example:  (infinity)⁰

Example:  infinity - infinity 

lim x -> 1⁺ (1/(x² - 1) - 1/lnx)  = lim x -> 1⁺  [lnx - (x² - 1)]/[(x² - 1)lnx]

= lim x -> 1⁺ [1/x - 2x]/[2xlnx + (x - 1)/x) = (1 - 2)/0 which is undefined.

Exercise:  lim x -> 0⁺ x^x