1 / 11

Section 4.4

Section 4.4. Indeterminate Forms and L’Hospital’s Rule. Remember Limits?. As x approaches a certain number from both sides – what does y approach? In order for them limit to exist you must approach the same y from both sides of x. How to find Limits. Direct Substitution: Factor Cancel:

ezhno
Download Presentation

Section 4.4

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. Section 4.4 Indeterminate Forms and L’Hospital’s Rule

  2. Remember Limits? As x approaches a certain number from both sides – what does y approach? In order for them limit to exist you must approach the same y from both sides of x

  3. How to find Limits Direct Substitution: Factor Cancel: Rationalize:

  4. How to find Limits (cont.) Squeeze Theorem Trig Substitution

  5. Example 1 Direct substitution gives which we call the indeterminate form. To fix an indeterminate we divide by the highest power of x in the denominator

  6. Example 2 The limit of a function at is it’s horizontal asymptote

  7. Example 2 (Cont.)

  8. Not all indeterminate forms can be evaluated by algebraic manipulation. This is particularly true when both algebraic and transcendental functions are involved. In cases like these, use L’Hospital’s Rule

  9. L’Hospital’s Rule Under certain conditions the limit of the quotient is determined by the limit of Let f and g be functions that are differentiable on an open interval (a,b) containing c, except possibly at c itself. If then provided the limit on the right exist (or is infinite).

  10. Example 1 Direction Substitution gives so we are allowed to use L’Hospital’s Rule

  11. Example 2 Direction Substitution gives so we are allowed to use L’Hospital’s Rule

More Related