Download presentation

Presentation is loading. Please wait.

Published byJordan Nazworth Modified over 2 years ago

1
Section 2.9 Linear Approximations and Differentials Math 1231: Single-Variable Calculus

2
Linear Approximation Use the tangent line at (a, f(a)) as an approximation to the curve y = f(x) when x is near a. An equation of this tangent line is y = f(a) + f ’ (a)(x-a) and the approximation f(x) ≈ f(a) + f ’ (a)(x-a) is called the linear approximation or tangent line approximation of f at a. The linear function L(x) = f(a) + f ’ (a)(x-a) is called the linearization of f at a.

3
Examples

4
Asymptotical Identity sin(x) ≈ x cos(x) ≈ 1 When x is close to 0.

5
Differentials dy = f’(x) dx

Similar presentations

OK

Section 3.9 - Differentials. Local Linearity If a function is differentiable at a point, it is at least locally linear. Differentiable.

Section 3.9 - Differentials. Local Linearity If a function is differentiable at a point, it is at least locally linear. Differentiable.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on centring sheet Ppt on acid-base indicators tea Ppt on a secure crypto biometric verification protocol Ppt on chapter natural resources Ppt on conservation of forest and wildlife Ppt on eisenmenger syndrome treatment Ppt on steve jobs leadership Ppt on object-oriented technologies Ppt on beer lambert law examples Ppt on power sharing in democracy in america