# chad_sheet - B A x y relative maximum f '(x)=0 zero f (x)=0...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: B A x y relative maximum f '(x)=0 zero f (x)=0 relative minimum f '(x)=0 absolute maximum inflection point f ''(x)=0 a b c d e k b f '(x) d e +- + c f ''(x) e +- Area = ∫ f (x) dx a b Domain: ( - ∞ , e ]- ∞ < x ≤ e Range: ( - ∞ , k ]- ∞ < y ≤ k Sample Function f(x) sin ² x + cos ² x = 1 1 + tan ² x = sec ² x 1 + cot ² x = csc ² x cos (a+b) = cos a cos b - sin a sin b sin (a+b) = sin a cos b + cos a sin b cos (a - b) = cos a cos b + sin a sin b sin (a - b) = sin a cos b - cos a sin b transcendental integrals Double Angle Identities sin 2x = 2 sin x cos x cos 2x = cos ² x - sin ² x cos ² x = 1+ cos 2x 2 sin ² x = 1- cos 2x 2 Odd/Even Identities sin (- x) = - sin x cos (- x) = cos x tan (- x) = - tan x cot (- x) = - cot x sec (- x) = sec x csc (- x) = - csc x C B A a c b x sin x =a/c= opposite/hypotenuse cos x = b/c = adjacent/hypotenuse sec x = c/b = hypotenuse/adjacent csc x = c/a = hypotenuse/opposite tan x = a/b = sin x/cos x = opposite/adjacent cot x = b/a = cos x/sin x = adjacent/opposite trig in a nutshell logs in a nutshell personal notes ln (xy) = ln x + ln y ln (x/y) = lnx - lny ln x = n ln x ln e = e = x ln 1 = 0 ln e = 1 ln x lim n → ∞ n = e (1+ ) 1 n if: a = x log x = b b a e 10 log x = log x log x = ln x 3 step test for continuity: 1. f(c) exists 2. lim exists x->c 3. lim = f(c) x->c derivatives integration by parts velocity & motion volumes & areas disc & shell methods partial fractions trig substitutions transcendental derivatives Product Rule f ' (u v) = udv + vdu Chain Rule (f o g)' = f ' g ' Quotient Rule f ' ( ) = v du - u dv v ² u v (Lo D Hi minus Hi D Lo over Lo Lo) f (x + h) - f (x) h f ' (x) = lim h -> 0 definition of the derivative: Power Rule f ' ( x ) = c x Addition Rule f ' (u + v) = f ' u + f ' v c c -1 Mean Value Theorem f (b) - f (a) b - a = f ' (c) l’Hôpital’s Rule When lim f (x) g(x) x → a lim f ' (x) g ' (x) x → a = ∞ ∞ lim f (x) g(x) x → a = OR trig derivatives Standard Trig (d/dx)(csc u) = - csc u cot u (d/dx)(sec u) = sec u tan u (d/dx)(cot u) = - csc ² u (d/dx)(tan u) = sec ² u (d/dx)(cos u) = - sin u (d/dx)(sin u) = cos u d dx 1 du u dx ln u = d dx du dx e = e u u d dx du dx a = a ln a u u 1 1 f (x) = a x f (x) = log x a (Use h(b 1 +b 2 )/2 for trapezoids of different height) ∫ f (x) dx = F(a) - F(b) where F is the antiderivative of f a b integrals Power Rule: ∫ x dx = x +C a+1 x ≠ - 1 a a+1 Average Value f (x) dx Avg. (f (x)) = a b 1 ....
View Full Document

## This note was uploaded on 04/16/2008 for the course PHYS 40 taught by Professor Ellison during the Winter '08 term at UC Riverside.

### Page1 / 2

chad_sheet - B A x y relative maximum f '(x)=0 zero f (x)=0...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online