1 / 18

What You NEED To Know In Calculus

What You NEED To Know In Calculus. The Fundamental Theorem of Calculus. b. ∫. f (x)dx = F(b) – F(a). a. The fundamental theorem of calculus is used to evaluate definite integrals using antiderivatives.

diata
Download Presentation

What You NEED To Know In Calculus

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. What You NEED To Know In Calculus

  2. The Fundamental Theorem of Calculus

  3. b ∫ f(x)dx = F(b) – F(a) a The fundamental theorem of calculus is used to evaluate definite integrals using antiderivatives. It is central to the evaluation of integrals, allowing you to find the area under a curve or between two functions. If f is continuous at every point of [a, b], and if F is any antiderivative of f on [a, b] then:

  4. 3 3 ∫ ∫ (x3 + 1)dx (x3 + 1)dx -1 -1 ] 3 x4 4 -1 Example: Find Antiderivative evaluated at 3 = + x Antiderivative evaluated at -1 Antiderivative of (x3 + 1) (81 / 4 + 3) – (1 / 4 – 1) = = 24

  5. The Quotient Rule

  6. This rule is used in calculus when you want to find the derivative of a function that is a quotient. Hi Lo LoDeHi-HiDeLo Lo2

  7. Example: Find f’(x)=x -1 x +1 Hi=x -1 DeHi=2x Lo=x +1 DeLo=2x F’(x)= (x +1) (2x)-(x -1)(2x) (x +1)2 2 2 2 2 2 2 2

  8. The Chain Rule

  9. The Chain Rule applies whenever there is a function that is formed from two simpler function. F(x)= g(h(x)) >>>> F(x)= g’(h(x)) h’(x)

  10. Example: (sin(2x))’=2sin(x)cos(x) (sin(2x))’=2(sin’(x)cos(x)+sin(x)cos’(x)) (sin(2x))’=2(cos2(X)-sin2(x)) (sin(2x))’= 2cos(2x)

  11. Can You Jerk???!

  12. Jerk! f’’’(x)

  13. To get the Jerk of an equation is to take the derivative of that equation 3 separate times. f’’’(x)

  14. Example: Find the Jerk of 4x5. 1st Der.: 20x4 2nd Der.: 80x3 3rd Der.: 240x2

  15. Works Consulted Finney, Ross, Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus. New Jersey: Pretince Hall, 2003. Print. Kahn, David S. Cracking the AP Calculus AB & BC Exams. New York: Random House, 2009. Print.

More Related