Integral calculus - Study guides, Revision notes & Summaries

Limit Definition of Derivative Mean Value Theorem If f(x) is defined and continuous on [a,b] and differentiable on (a,b) then there is at least one point where f'(c) = f(b)-f(a)/b-a A function is continuous at a point x=a if: a) f(a) is defined b) Limit as x approaches a of f(x) c) Limit as x approaches a of f(x) is equal to f(a) Fundamental Theorem of Calculus (P1) If f is continuous on [a,b] F(x) = ∫f(x) and both are continuous on [a,b] F(x) is differentiable on ...

AP Calculus AB Concepts Critical Points - Answer>>where f'(x)=0 or f'(x) is undefined Splitting the Fraction - Answer>>a+b+c/d = a/d + b/d + c/d Riemann Sums - Answer>>MRAM, RRAM, LRAM Displacement (change in position) - Answer>>The integral from a to b of v(t) dt Total distance traveled - Answer>>The integral from a to b of | v(t) | dt

evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...

Student Solutions Manual to accompany Calculus for Business, Economics, and the Social and Life Sciences Tenth Edition, by Laurence D. Hoffman CONTENTS Chapter 1 Functions, Graphs, and Limits 1 1.1 Functions 1 1.2 The Graph of a Function 6 1.3 Linear Functions 14 1.4 Functional Models 19 1.5 Limits 26 1.6 One-Sided Limits and Continuity 30 Checkup for Chapter 1 33 Review Problems 36 Chapter 2 Differentiation: Basic Concepts 43 2.1 The Derivative 43 2.2 Techniques of Differentia...

How do rationalism and empiricism differ? - Rationalism seeks to establish the validity or invalidity of a proposition through logic whereas empiricism relies on sensory observation. According to Kuhn, in which state of scientific development do a number of competing viewpoints exist? - the preparadigmatic stage A psychologist who argues that human behavior is a product of our evolutionary heritage subscribes to which type of determinism? - biological determinism Descartes and Freud bel...

True - A student's t-test is a means test. True - A standard normal curve represents a family of curves described by parametric statistics and is studied using integral calculus. True - A paradigm was once a paradox False - A random sample usually provides bias results False - Sample size is the most important aspect to any experiment

AP Calculus BC Series Tests + Power Series N-th term test limₙ→∞ ∑aₙ ≠ 0 is absolute divergence *CANNOT show convergence Integral Test ∫∞,n f(x) converges/diverges Harmonic series ∑ 1/n, diverges P-series ∑1/pⁿ ⁿ>1 is convergence ⁿ≤1 is divergence Direct comparison test 0<aₙ≤bₙ AND bₙ converges is convergence 0<bₙ≤aₙ AND bₙ diverges is divergence *inconclusive if conditions not met

Preface page ix 1 Preliminary algebra 1 2 Preliminary calculus 17 3 Complex numbers and hyperbolic functions 39 4 Series and limits 55 5 Partial differentiation 71 6 Multiple integrals 90 7 Vector algebra 104 8 Matrices and vector spaces 119 9 Normal modes 145 10 Vector calculus 156 11 Line, surface and volume integrals 176 v CONTENTS 12 Fourier series 193 13 Integral transforms 211 14 First-order ODEs 228 15 Higher-order ODEs 246 16 Series solutions of ODEs 269 17 Eigenfuncti...

PSYC 375 Midterm Exam Questions With 100% Correct Answers How do rationalism and empiricism differ? - answerRationalism seeks to establish the validity or invalidity of a proposition through logic whereas empiricism relies on sensory observation. According to Kuhn, in which state of scientific development do a number of competing viewpoints exist? - answerthe preparadigmatic stage A psychologist who argues that human behavior is a product of our evolutionary heritage subscribes to which ...