| The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages. |
|
Home  Limits, Analytic Geometry, and Approximations L'Hospitals Rule L'Hospitals Rule for ∞/∞ |
|||||
 Search the VIAS Library | Index
|
  |
||||
L'Hospitals Rule for ∞/∞
L'HOSPITAL'S RULE FOR ∞/∞ Suppose c is a real number, and in some deleted neighborhood of c, f'(x) and g'(x) exist and g'(x) ≠ 0. Assume that limx→c f(x) = ∞, limx→c g(x) = ∞. If
The rule for ∞/∞ is exactly the same, word for word, as the rule for 0/0, except that 0 is replaced by ∞. We omit the proof, which is more difficult in the case ∞/∞. Actually, the assumption limx→c f(x) = ∞ is not needed. Again, l'Hospital's Rule for ∞/∞ also holds for the other types of limits, x → c+, x → c-, x → ∞, x → -∞.
|
|||||
| Home Limits, Analytic Geometry, and Approximations L'Hospitals Rule L'Hospitals Rule for ∞/∞ |
|
||||
exists or is infinite, then
Last Update: 2006-11-14