4.5 - x = 2 . Calculus Section 4.5 Page25 b) How accurate...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus Section 4.5 Page 24 4.5 Linearization Linear Approximation Exploration Approximating with Tangent Lines Let f x ( ) = x 2 . 1. Show that the line tangent to the graph of f at the point 1, 1 ( ) is y = 2 x - 1. 2, Set y 1 = x 2 and y 2 = 2 x - 1. Zoom in on the two graphs at 1, 1 ( ) . What do you see? Definition Linearization If f is differentiable at x = a , then the approximating function L x ( ) = f a ( )+ f a ( ) x - a ( ) is the linearization of f at a . Example 1 a) Find the linearization L x ( ) (or linear approximation) of f x ( ) = 1 + x at x = 0 . b) How accurate is the approximation L 0 + 0.1 ( ) ≈ f 0 + 0.1 ( ) for values of x near 0? Example 2. a) Find the linearization L x ( ) of f x ( ) = cos x at
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x = 2 . Calculus Section 4.5 Page25 b) How accurate is the approximation L 2 + 0.1 f 2 + 0.1 for values of x near 2 ? Definition Differentials Let y = f x ( ) be a differentiable function. The differential dx is an independent variable. The differential dy is defined as: dy = f x ( ) dx Example 3. Find dy and evaluate dy for the given value of x and dx . What does this mean geometrically in a)? a) y = x 2 x = 1, dx = 0.01 b) y = x 1-x 2 x = 0, dx = -0.2 Assignment III-5 Pages 229 230 #1 5 all, 19, 21, 23...
View Full Document

Page1 / 2

4.5 - x = 2 . Calculus Section 4.5 Page25 b) How accurate...

This preview shows document pages 1 - 2. Sign up to view the full document.

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