Chapter 2 Section 6

# Chapter 2 Section 6 - -= =-→ → → → θ Example 8...

This preview shows pages 1–11. Sign up to view the full content.

1 Chapter 2 Section 6 Limits of Trig Functions and the Squeeze Theorem

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

View Full Document
2 Objectives 1. Find limits involving trig functions. 2. Find limits using the Squeeze Theorem
3 Notation review: sin 2 (x) = [sin(x)] 2 sin x 2 = sin(x 2 ) [sin(x)] -1 = 1/sin(x) = csc(x) sin -1 (x) = arcsin(x)

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

View Full Document
4 x x Consider x ) sin( lim 0 x -1 -0.5 -0.1 -0.01 0 0.01 0.1 0.5 1 sin(x)/x 0.84 0.96 0.998 0.99998 dne 0.99998 0.998 0.96 0.84 x -1 -0.5 -0.1 -0.01 0 0.01 0.1 0.5 1 [1-cos(x)]/x -0.46 -0.24 -0.05 -0.005 dne 0.005 0.05 0.24 0.46 Note: “x” must be in radians.
5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y y = sin(x)/x 1 ) sin( lim 0 = x x x 0 1 0 = - x x x ) cos( lim -4 -3 -2 -1 1 2 3 4 5 -3 -2 -1 1 2

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

View Full Document
6 3 2 6 4 lim 6 1 4 1 lim 6 6 ) 6 sin( 4 4 ) 4 sin( lim ) 6 sin( ) 4 sin( lim : 0 0 0 0 = = = = = x x x x x x x x x x x x x x Example
7 0 1 0 lim sin cos 1 lim 1 1 sin cos 1 lim sin cos 1 lim : 0 0 0 0 = = - = ×

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -= =-→ → → → θ Example 8 Example: Given 3x < f(x) < x 3 + 2 for 0< x< 2, find lim x 1 f(x) We must use the Squeeze Theorem. 9 Squeeze Theorem If L (x) < f(x) < U (x) when x is near “c” except possibly at “c” and lim x c L (x) = lim x c U (x) = N then lim x c f(x) = N. 10 Example: Given 3x < f(x) < x 3 + 2 for 0< x< 2, find lim x 1 f(x) lim x 1 3x = 3 lim x 1 x 3 + 2 = 3 therefore, lim x 1 f(x) = 3 by the Squeeze Theorem 11 ) sin( lim : x x e x Example π + →...
View Full Document

## This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

### Page1 / 11

Chapter 2 Section 6 - -= =-→ → → → θ Example 8...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online