1 / 18

Section 4.5

Section 4.5. Limits “at Infinity”. Limits “at Infinity”. Deal with the end behavior of a function. Horizontal Asymptotes. Remember these from MTH 112?. Critical Info. What happens in the sequences below? What is equal to?. Additional Example 3. Find the limits. Section 4.6.

maya
Download Presentation

Section 4.5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 4.5 Limits “at Infinity”

  2. Limits “at Infinity” • Deal with the end behavior of a function.

  3. Horizontal Asymptotes • Remember these from MTH 112?

  4. Critical Info • What happens in the sequences below? • What is equal to?

  5. Additional Example 3 Find the limits.

  6. Section 4.6 A Summary of Curve Sketching

  7. Additional Example -intercepts: -intercept: First derivative: Second derivative: End behavior: Critical numbers: Inflection pts.:

  8. Section 4.7 Optimization Problems

  9. Example 1 An open box of maximum volume is to be made from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and turning up the sides. What is the maximum volume of the box?

  10. Example 2 Find two positive numbers such that the sum of the first number and twice the second number is 108 and the product is a maximum.

  11. Example 3 Find the length and width of a rectangle that has a perimeter of 80 meters and a maximum area.

  12. Example 4 Find the length and width of a rectangle that has an area of 32 square feet and a minimum perimeter.

  13. Example 5 Which points on the graph of are closest to the point ?

  14. Example 6 A farmer plans to fence in a rectangular pasture adjacent to a river. The pasture must contain 245,000 sq. meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river?

  15. Example 7 A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet.

  16. Example 8 A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent.

More Related