1 1 A Preview of Calculus and 1
- Slides: 17
1. 1 A Preview of Calculus and 1. 2 Finding Limits Graphically and Numerically
Objectives Understand what calculus is and how it compares to precalculus. Estimate a limit using a numerical or graphical approach. Learn different ways that a limit can fail to exist.
Swimming Speed: Taking it to the Limit Questions 1 -5
Preview of Calculus Diagrams on pages 43 and 44
Two Areas of Calculus: Differentiation Animation of Differentiation
Two Areas of Calculus: Integration Animation of Integration
Limits Both branches of calculus were originally explored using limits. Limits help define calculus.
1. 2 Finding Limits Graphically and Numerically
Find the Limit x . 75 . 999 1 1. 001 1. 25 f(x) 2. 313 2. 710 2. 970 2. 997 ? 3. 003 3. 310 3. 813 x approaches 1 from the left x approaches 1 from the right Limits are independent of single points.
Exploration (p. 48) From the graph, it looks like f(2) is defined. Look at the table. On the calculator: tblstart 1. 8 and ∆Tbl=0. 1. Look at the table again. What does f approach as x gets closer to 2 from both sides?
Example Look at the graph and the table.
Example Limits are NOT affected by single points!
Three Examples of Limits that Fail to Exist If the left-hand limit doesn't equal right-hand limit, the two-sided limit does not exist.
Three Examples of Limits that Fail to Exist If the graph approaches ∞ or -∞ from one or both sides, the limit does not exist.
Three Examples of Limits that Fail to Exist Look at the graph and table. As x gets close to 0, f(x) doesn't approach a number, but oscillates back and forth. If the graph has an oscillating behavior, the limit does not exist.
Limits that Fail to Exist f(x) approaches a different number from the right side of c than it approaches from the left side. f(x) increases or decreases without bound as x approaches c. f(x) oscillates as x approaches c.
Homework 1. 2 (page 54) #5, 7, 15 -23 odd
- What is thesis statement
- Summary of thesis statement
- Thesis and preview statement example
- Classic trio' of selection techniques
- Review and preview
- Realistic job preview pros and cons
- Test prep preview
- Test prep preview
- Test prep preview
- Test prep preview
- Sccm technical preview
- Startling statement introduction examples
- Test prep preview
- Nnn preview
- The selection preview
- Test prep preview
- The four agreements preview
- Test prep preview