25-LHopital

25-LHopital - Math 1a LHopitals Rule Fall, 2009...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 1a LHopitals Rule Fall, 2009 & $ % Indeterminate Forms Were considering lim x a f ( x ) g ( x ) . We begin with several indeterminate forms: Type : lim x a f ( x ) = 0 and lim x a g ( x ) = 0 Type : lim x a f ( x ) = or- and lim x a g ( x ) = or- LH opitals Rule (or LHospitals Rule ) is: if f and g are differentiable and g ( x ) is not zero near a (but g ( a ) may be zero). Then if the limit (on the left, below) is of indeterminate form 0 / 0 or / , then lim x a f ( x ) g ( x ) = lim x a f ( x ) g ( x ) provided the limit on the right exists (or is + or- ). 1 For each of the following, verify that the given limit is in an indeterminate form, then use LH opitals Rule (if possible) to determine the limit. (a) lim x sin( x ) x (b) lim x sin( x ) x 2 (c) lim x + sin( x ) x (d) lim x 1 x 2- 1 ln( x ) (e) lim x e x- 1 x (f) lim x ln( x ) x (g) lim x...
View Full Document

This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

Page1 / 4

25-LHopital - Math 1a LHopitals Rule Fall, 2009...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online