1 / 5

L’Hospital’s Rule

L’Hospital’s Rule. L’Hospital’s Rule: In cases in which an indeterminate form occurs, if the limit of f(x)/g(x) exists it is equivalent to the limit of f’(x)/g’(x). Indeterminate forms: 0/0, ∞/∞, and -∞/-∞. -2 2 -4=0 -2+2=0. f’(x)=2x g’(x)=1. 4. e ∞ =∞ 5∞ 2 =∞. f’(x)=e x g’(x)=10x.

justin
Download Presentation

L’Hospital’s Rule

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. L’Hospital’s Rule

  2. L’Hospital’s Rule: In cases in which an indeterminate form occurs, if the limit of f(x)/g(x) exists it is equivalent to the limit of f’(x)/g’(x). Indeterminate forms: 0/0, ∞/∞, and -∞/-∞

  3. -22-4=0 -2+2=0 f’(x)=2x g’(x)=1 4

  4. e∞=∞ 5∞2 =∞ f’(x)=ex g’(x)=10x f’’(x)=ex g’’(x)=10 =∞

  5. Indeterminate Products If f(x)*g(x) results in the indeterminate form 0*∞, by rearranging the function to f/(1/g) or g/(1/f) we convert the product to the indeterminate form 0/0 or ∞/∞, and can use L’Hospital’s rule to evaluate the limit. Example limx->0+xlnx limx->0+x= 0 limx-> 0+lnx= ∞ If we evaluate the limit of each function, the product is the indeterminate form 0*∞. limx->0+lnx/(1/x) limx->-∞ (1/x)/(-1/x2) limx->0+-x2/x limx->0+-x = 0

More Related