Download presentation

Presentation is loading. Please wait.

Published byKorey Guest Modified over 6 years ago

1
Calculus Final Exam Review By: Bryant Nelson

2
Common Trigonometric Values x-value0π/6π/3π/22π/35π/6π7π/64π/33π/25π/311π/62π sin(x)0½1½0-½-½0 cos(x)1½0-½-½0½1

3
Special Trigonometric Limits lim h 0 sin(h) h = ? 1 lim h 0 cos(h) - 1 h = ? 0

4
Differentiation Rules Definition of a Derivative: f’(x) = lim Δx 0 f(x+Δx) – f(x) Δx

5
Differentiation Rules cont. Product Rule: (f·g)’ = f’·g + f·g’ Quotient Rule: (f/g)’ = (f’·g - f·g’)/g 2 Natural Log Rule: d/dx(ln(u)) = (1/u) ·du/dx Exponential Rules: d/dx(℮ u ) = (℮ u ) ·du/dx d/dx(b u ) = (b u ) ·ln(b)·du/dx ·

6
Differentiation Rules cont. d/dx(sin(u)) =(cos(u))du/dx Trigonometric Rules d/dx(cos(u)) =(-sin(u))du/dx d/dx(tan(u)) =(sec 2 (u))du/dxd/dx(cot(u)) =(-csc 2 (u))du/dx d/dx(sec(u)) =(sec(u)tan(u))du/dxd/dx(csc(u)) =(-csc(u)cot(u))du/dx

7
Differentiation Rules cont. d/dx(sin -1 (u)) =(1/(√1-u 2 ))du/dx Inverse Trigonometric Rules d/dx(cos -1 (u)) =(-1/(√1-u 2 ))du/dx d/dx(tan -1 (u)) =(1/(1+u 2 ))du/dxd/dx(cot -1 (u)) =(-1/(1+u 2 ))du/dx d/dx(sec -1 (u)) =(1/(|u|·√u 2 -1))du/dxd/dx(csc -1 (u)) =(-1/(|u|·√u 2 -1))du/dx

8
Integration Rules Power Rules: ∫(u n ·du) = (u n+1 )/(n+1) +C; only while n ≠ -1 ∫(u -1 ·du) = ln(|u|) +C Exponential Rules: ∫(℮ u ·du) = ℮ u +C ∫(b u ·du) = b u /ln(b) - u +C, b≠1 Logarithmic Rule: ∫(ln(u)·du) = u·ln(u) - u +C, u>0

9
Integration Rules cont. ∫(sin(u)·du) =-cos(u) + C Trigonometric Rules ∫(cos(u) ·du) =sin(u) + C ∫(tan(u) ·du) =-ln(|cos(u)|) + C∫(cot(u) ·du) =ln(|sin(u)|) + C ∫(sec(u) ·du) =ln(|sec(u) + tan(u)|) + C∫(csc(u) ·du) =ln(|csc(u) + cot(u)|) + C

10
Integration Rules cont. Trigonometric Rules cont. ∫(sec 2 (u) ·du) =tan(u) + C∫(csc 2 (u) ·du) =-cot(u) + C ∫(sec(u)tan(u) ·du) =sec(u) + C∫(csc(u)cot(u) ·du) =-csc(u) + C

11
Summation Formulas n ∑ n K=1 1 = (n(n+1))/2 ∑ n K=1 k = (n(n+1)(2n+1))/6 ∑ n K=1 k 2 = (n 2 (n+1) 2 )/4 ∑ n K=1 k 3 =∑ n K=1 c·a k =∑ n K=1 akak c·c·

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google