Download presentation

Presentation is loading. Please wait.

Published byTrinity Callahan Modified over 3 years ago

2
An Introduction to Limits Objective: To understand the concept of a limit and To determine the limit from a graph

3
Calculus centers around 2 fundamental problems – 1)The tangent line- differential calculus P Q Instantaneous rate of change (Slope at a point) (Slope between 2 points)

5
2) The area problem- integral calculus Uses rectangles to approximate the area under a curve.

6
Limits: Yes – finally some calculus! Objective: To understand the definition of a limit and to graphically determine the left and right limits and to algebraically determine the value of a limit. If the function f(x) becomes arbitrarily close to a single number L (a y-value) as x approaches c from either side, then lim x c f(x) = L. *A limit is looking for the height of a curve at some x = c. *L must be a fixed, finite number. One-Sided Limits: lim x c+ f(x) =L 1 Height of the curve approach x = c from the right lim x c- f(x) =L 2 Height of the curve approach x = c from the left

7
Definition of Limit: If lim x c+ f(x) = lim x c- f(x) = L then, lim x c f(x)=L (Again, L must be a fixed, finite number.) f(2) = f(4) = Examples:

8
f(4) = f(0) = f(6) = f(3) =

9
Basic Limits (for the book part) lim x 4 2x – 5 = lim x -3 x 2 = lim x cos x = lim x 1 sin =

10
Important things to note: The limit of a function at x = c does not depend on the value of f(c). The limit only exists when the limit from the right equals the limit from the left and the value is a FIXED, FINITE #! A common limit you need to memorize: (see proof page 65 ) Limits fail to exist: (ask for pictures) 1. Unbounded behavior – not finite 2. Oscillating behavior – not fixed 3. - fails def of limit Do you understand how to graphically find a limit? HW: 1.2 1-31(odd) Use your calculator!

Similar presentations

OK

Aim: What do slope, tangent and the derivative have to do with each other? Do Now: What is the equation of the line tangent to the circle at point (7,

Aim: What do slope, tangent and the derivative have to do with each other? Do Now: What is the equation of the line tangent to the circle at point (7,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Conceptual architecture view ppt on iphone Ppt on standing order edinburgh Ppt on standing order definition Ppt on social contract theory example Marketing mix ppt on sony tv Ppt on as 14 amalgamation Ppt on review of related literature in research Ppt on shell scripting linux Ppt on edge detection test Ppt on marketing management on jeans