29 - L'hopital

29 - L'hopital - lim x bx 2 + 4 x-tan 4 x x 3 is defined....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Indeterminate Forms and L’Hopital’s Rule Suppose we want to find lim x 0 sin x x . If we substitute 0 for x, we get 0 0 . The limit may or may not exist. It’s indeterminate. (We can’t determine the limit.) Any limit of the form lim x a f ( x ) g ( x ) 0 0 is called an indeterminate form of type 0 0 . We call the form lim x a f ( x ) g ( x ) an indeterminate form of type . L’Hopital’s Rule: If lim x a f ( x ) 0 lim x a g ( x ) or if lim x a f ( x ) lim x a g ( x ) then lim x a f ( x ) g ( x ) lim x a f ( x ) g ( x ) Ex. lim x 0 sin x x
Background image of page 1

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

View Full DocumentRight Arrow Icon
Ex. lim x 0 e x - 1 sin(2 x ) Ex. lim x 1 1 - x ln x 1 cos( x ) Ex. lim x e x x 2 x
Background image of page 2
Ex. Determine the value of b for which
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lim x bx 2 + 4 x-tan 4 x x 3 is defined. Products Ex. lim x -x 2 e x If we have lim x a f ( x ) g ( x ) , rewrite the limit as lim x a f ( x ) 1 g ( x ) or lim x a g ( x ) 1 f ( x ) . Do: 1. lim x sin 2 x x cos x 2. lim x 1 ln x x-1 2 3. lim x 3 x csc 2 x 4. Determine the value of b for which lim x bx + sin 5 x x 2 is defined....
View Full Document

This note was uploaded on 10/16/2009 for the course MATH 1206 taught by Professor Llhanks during the Spring '08 term at Virginia Tech.

Page1 / 4

29 - L'hopital - lim x bx 2 + 4 x-tan 4 x x 3 is defined....

This preview shows document pages 1 - 4. Sign up to view the full document.

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