Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Lesson 13 derivative of hyperbolic ... by Rnold Wilson 221 views
- Complete filming planning sheet by lancechirume 105 views
- Derivative and Integeration Formulas by Muhammad Talha Za... 218 views
- Merchant banking guidelines by Taher Ahmed 4569 views
- Sebi guidelines for merchant bankers by SHAMEEM ET 2728 views
- Merchant banking in india by Aditya Kumar 54368 views

No Downloads

Total views

1,568

On SlideShare

0

From Embeds

0

Number of Embeds

82

Shares

0

Downloads

23

Comments

0

Likes

1

No embeds

No notes for slide

- 1. Develop properties of hyperbolic functions Differentiate and integrate hyperbolic functions Develop properties of inverse hyperbolic functions Differentiate and integrate inverse hyperbolic functions Whew! Just a quick look at hyperbolic functions.
- 2. A brief look at hyperbolic functions: The name came from comparison of the area of semicircular regions with the area underneath a hyperbola.
- 3. Note that the graphs of sinh x can be obtained by addition of and . Similar things can be said about cosh x
- 4. <ul><li>Here are some youtube videos that were helpful with pronunciation and with interesting things about the hyperbolic functions: </li></ul><ul><li>http://youtu.be/vqfVKsBkB1s How the Arch got its shape (2:59) </li></ul><ul><li>http://youtu.be/uW30SVZ68cU Hyperbolic Functions NJIT (7:16) </li></ul><ul><li>http://youtu.be/er_tQOBgo-I Hyperbolic Trig Functions MIT (13:25) </li></ul>
- 5. Many of the trigonometric identities that you know and love have corresponding hyperbolic identities. In order to not mess with your head, I am not requiring you to memorize these for the test, but instead will provide you with a cheat sheet that will include definitions, graphs, identities, derivatives, integration, and like things for the inverse hyperbolic functions. Comparing to the trig identity cos 2 x + sin 2 x = 1,
- 6. Kind of mind blowing, the similarities. But remember, they are related to exponential growth and decay, e x and e -x .
- 7. The derivatives of sinh x and cosh x are written in terms of e x and e -x so their derivatives are easily found.
- 8. Ex 1 p391 Differentiation of Hyperbolic Functions product
- 9. Ex 2 p. 391 Finding Relative Extrema Find the relative extrema of f(x) = xsinh(x – 1) – cosh(x– 1) f ’(x) = xcosh(x – 1) + sinh(x – 1)(1) –-sinh(x –1) = xcosh(x – 1) f ‘(x)= 0 when x = 0 By the first derivative test, x = 0 gives a relative min, so (0, -cosh(-1)) is a relative minimum. Approximately (0, -1.543) Cosh, sinh, and tanh can be found in your catalog. The others must be defined using cosh, sinh, or tanh.
- 10. Ex 3 p. 391 Hanging Power Cables and Catenaries When a uniform flexible cable, such as a telephone wire, is suspended from two points that are at the same height, it takes the shape of a catenary . The way a necklace hangs is also a catenary. Power cables are suspended between two towers, forming the catenary shown in the figure. The equation for this catenary is y = a cosh (x/a) The distance between the two towers is 2b. Find the slope of the catenary at the point where the cable meets the right-hand tower. y‘=a sinh(x/a)*(1/a)=sinh(x/a). At the point where the cable meets the right-hand tower, x = b. So at the point (b, a cosh(b/a)), the slope (coming from the left) is m = sinh (b/a)
- 11. 5.8a p. 396/ 1-33 odd, 34, 37

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment