AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

Natural logarithm

Population Growth Questions

Subject: 
Chemistry
Rating: 
0
No votes yet
Tags: 
logarithms
Population ecology
Exponentials
Demography
population
Population dynamics
Exponential growth
Logistic function
Natural logarithm
Doubling time

Bio 270 Practice Population Growth Questions 1 Population Growth Questions Answer Key 1. Distinguish between exponential and logistic population growth. Give the equations for each. Exponential growth is continuous population growth in an environment where resources are unlimited; it is density-independent growth. dN/dt = rN where, dN/dt = change in population size; r = intrinsic rate of increase (= per capita rate of increase and equals birth rate minus death rate); N = population size. Nt = Noert where, Nt = population size at time t; No = original population size, r = intrinsic rate of increase and t = time Logistic growth is continuous population growth in an environment where resources are

2_logarithmic_functions_1

Subject: 
Art History
Rating: 
0
No votes yet
Tags: 
logarithms
Logarithm
Natural logarithm
Binary logarithm
Log–log plot
Exponential function
Common logarithm
Exponentiation
Logarithmic differentiation
Logarithmic units

Section 3.2 Logarithmic Functions 1 Section 3.2 Logarithmic Functions (Complete problems in purple before class) Definition: Logarithmic Function For a > 0 and a ? 1, the logarithmic function with base a denoted f ( x) = log a ( x), where ? = log?(?) if and only if ? ? = ? Note that log a( 1) = 0 for any base a, because a 0 = 1 for any base a. ? There are two bases that are used more frequently than others; they are 10 and e. ? The notation log 10( x) is abbreviated log( x) and log e( x) is abbreviated ln( x), which are called common logarithms and natural logarithms, respectively. Note: log x means x10log : base 10 ln e means xelog : base e One-to-One Property of Logarithms

Calculus AB #4

Subject: 
Calculus
Rating: 
0
No votes yet
Tags: 
trigonometry
Natural logarithm
Cofunction
Technology

Ws 4 ? TRIG VALUES Show your work in your NOTEBOOK! 1. Solve each such that 0 2x ?? ? . a. 3tan 3x ? b. 1sin 2x ? c. 3cos 2x ? d. tan 1x ? ? e. sin 1x ? ? f. cos 0x ? g. 2sin 2x ?? h. csc 2x ? ? i. 2 3sec 3x ? ? j. tan x is undefined. k. cot 0x ? 2. Solve each equation such that 0 2x ?? ? . a. 2cot cot 0x x? ? b. 22cos 7cos 4x x? ? c. 2 2cos sin sin 0x x x? ? ? d. 2 22sin 5sin 3sin 0x x x? ? ? e. 2sin 2cos 2x x? ? f. 24cos 1x ? g. 23cos 3 2sinx x? ? 3. RECALL! Evaluate each. a. 11sin 6 ? b. 3sin 2 ? c. cos? d. 2tan 3 ? e. csc 3 ? f. 4cos 3 ? 4. Solve each such that 0 2x ?? ? . Round each to 3 decimal places. a. sin 0.231x ? b. csc 2.675x ?? c. tan 0.219x ?? d. cot 1.290x ?

AP Calc Study Guide

Subject: 
Calculus
Rating: 
0
No votes yet
Tags: 
Calculus
Mathematical analysis
Mathematics
Differentiation rules
Integral calculus
Integration by parts
Integration by substitution
Product rule
Natural logarithm
Quotient Rule
derivative
Differential equation
education

Copyright 1996,1997 Elaine Cheong All Rights Reserved Study Guide for the Advanced Placement Calculus AB Examination By Elaine Cheong 1 Table of Contents INTRODUCTION 2 TOPICS TO STUDY 3 ? Elementary Functions 3 ? Limits 5 ? Differential Calculus 7 ? Integral Calculus 12 SOME USEFUL FORMULAS 16 CALCULATOR TIPS AND PROGRAMS 17 BOOK REVIEW OF AVAILABLE STUDY GUIDES 19 ACKNOWLEDGEMENTS 19 2 Introduction Advanced Placement1 is a program of college-level courses and examinations that gives high school students the opportunity to receive advanced placement and/or credit in college. The Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus, covering a full-year college mathematics course.

Trig formula sheet

Subject: 
Trigonometry
Rating: 
0
No votes yet
Tags: 
Mathematics
Mathematical analysis
Special functions
trigonometry
Analytic functions
logarithms
Exponentials
Natural logarithm
Inverse function
Trigonometric functions
Sine
Inverse trigonometric functions
education

All Rights Reserved: http://regentsprep.org Algebra 2 ? Things to Remember! Exponents: 0 1x ? 1m m x x ? ? ?m n m nx x x ?? ?( )n m n mx x? m m n n x x x ?? n n n x x y y ? ? ?? ?? ? ( ) ?n n nxy x y? Complex Numbers: 1 i? ? ; 0a i a a? ? ? 2 1i ? ? 14 2 1i i? ? ? divide exponent by 4, use remainder, solve. ( ) conjugate ( )a bi a bi? ? 2 2( )( )a bi a bi a b? ? ? ? 2 2a bi a b? ? ? absolute value=magnitude Logarithms log yby x x b? ? ? ln logex x? natural log e = 2.71828? 10log logx x? common log Change of base formula: log log logb a a b

Ch9 SG

Subject: 
Calculus
Rating: 
0
No votes yet
SocialTags: 
Calculus
Mathematical analysis
Mathematics
Differential calculus
Functions and mappings
Integral calculus
Ordinary differential equations
Differential equation
Derivative
Differential of a function
Multiple integral
Order of integration
Law
Tags: 
Calculus
Mathematical analysis
Mathematics
Ordinary differential equations
Differential calculus
Differentiation rules
Differential equations
Separation of variables
Natural logarithm
derivative
Differential of a function
Chain rule
law

372 CHAPTER 9 Mathematical Modeling with Differential Equations EXERCISE SET 9.1 1. y? = 2x2ex 3/3 = x2y and y(0) = 2 by inspection. 2. y? = x3 ? 2 sinx, y(0) = 3 by inspection. 3. (a) ?rst order; dy dx = c; (1 + x) dy dx = (1 + x)c = y (b) second order; y? = c1 cos t? c2 sin t, y?? + y = ?c1 sin t? c2 cos t+ (c1 sin t+ c2 cos t) = 0 4. (a) ?rst order; 2 dy dx + y = 2 ( ? c 2 e?x/2 + 1 ) + ce?x/2 + x? 3 = x? 1 (b) second order; y? = c1et ? c2e?t, y?? ? y = c1et + c2e?t ? ( c1et + c2e?t ) = 0 5. 1 y dy dx = x dy dx + y, dy dx (1? xy) = y2, dy dx = y2 1? xy 6. 2x+ y2 + 2xy dy dx = 0, by inspection. 7. (a) IF: ? = e3 ? dx = e3x, d dx [ ye3x ] = 0, ye3x = C, y = Ce?3x separation of variables: dy y = ?3dx, ln |y| = ?3x+ C1, y = ?e?3xeC1 = Ce?3x

Ch8 SG

Subject: 
Calculus
Rating: 
0
No votes yet
SocialTags: 
Integral calculus
U2
Environment
Health
Tags: 
Calculus
Mathematical analysis
Mathematics
Integral calculus
Integration by parts
Natural logarithm
Hyperbolic function
Trigonometric substitution
Integration by substitution
derivative
Integral of secant cubed
Sum rule in integration

317 CHAPTER 8 Principles of Integral Evaluation EXERCISE SET 8.1 1. u = 3? 2x, du = ?2dx, ? 1 2 ? u3 du = ?1 8 u4 + C = ?1 8 (3? 2x)4 + C 2. u = 4 + 9x, du = 9dx, 1 9 ? u1/2 du = 2 3 ? 9u 3/2 + C = 2 27 (4 + 9x)3/2 + C 3. u = x2, du = 2xdx, 1 2 ? sec2 u du = 1 2 tanu+ C = 1 2 tan(x2) + C 4. u = x2, du = 2xdx, 2 ? tanu du = ?2 ln | cosu |+ C = ?2 ln | cos(x2)|+ C 5. u = 2 + cos 3x, du = ?3 sin 3xdx, ? 1 3 ? du u = ?1 3 ln |u|+ C = ?1 3 ln(2 + cos 3x) + C 6. u = 3x 2 , du = 3 2 dx, 2 3 ? du 4 + 4u2 = 1 6 ? du 1 + u2 = 1 6 tan?1 u+ C = 1 6 tan?1(3x/2) + C 7. u = ex, du = exdx, ? sinhu du = coshu+ C = cosh ex + C 8. u = lnx, du = 1 x dx, ? secu tanu du = secu+ C = sec(lnx) + C 9. u = cotx, du = ? csc2 xdx, ? ? eu du = ?eu + C = ?ecot x + C
Subscribe to RSS - Natural logarithm

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!