# L06 - L6 The Tangent Line, Velocity Problems and Limits...

This preview shows pages 1–8. Sign up to view the full content.

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 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: L6 The Tangent Line, Velocity Problems and Limits Tangent line to a circle. Tangent line to a curve. Slope Approximate slope 1 Let f ( x ) = x 2 + 1. Find the equation of the tangent line at (1 , 2). (1 , 2) and (1 . 1 , 2 . 21) approximate m = (1 , 2) and (1 . 01 , 2 . 0201) approximate m = 2 Let P be (1 , 2) and Q be ( x,x 2 + 1) approximate m tangent m Equation: 3 Velocity Suppose an object is s ( t ) feet from its start at t seconds. Find the average velocity on the time interval from t = 2 to t = 2 + h seconds where s ( t ) = 3 t 2 . Average Velocity = 4 Find the velocity at the instant 2 seconds. Instantaneous velocity = 5 Def lim x a f ( x ) = L if we can make the values of f ( x ) arbitrarily close to L by taking x sufficiently close to a but not equal to a . f ( x ) as x Consider f ( x ) = x 2- 1 x- 1 . Find lim x a f ( x ). x f ( x ) x f ( x ) 6 Sketch f ( x ). Consider g ( x ) = x 2- 1 x- 1 x 6 = 1 3 x = 1 Sketch g ( x ) and find lim x 1 g ( x )....
View Full Document

## This note was uploaded on 01/13/2010 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

### Page1 / 14

L06 - L6 The Tangent Line, Velocity Problems and Limits...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online