# Calculus 1A, College of the Desert, Chapters1-4.txt

 The flashcards below were created by user Mattyj1388 on FreezingBlue Flashcards. ﻿Lim F(x) = L x-->a We say "the limit of F(x), as "x" approaches "a", equals "L".If we can make the values of F(x) arbitrarily close to "L" (as close to "L" as we like) by taking "x" to be sufficiently vlose to "a" ( on either side of "a") but not equal to "a". (page 88) Function A function "F" is a rule that assigns to each element "x" in a set "D" exactly one element, called F(x), in a set "E". Increasing F(x1) < F(x2) whenever x1 < x2 in I. (page 20) Decreasing F(x1) > F(x2) whenever F(x1) > F(x2) in I. (Page 20) d/dx (sin x) = Cos x (page 193) d/dx (cos x) = -sin x (page 193) d/dx (tan x) = Sec2 x (page 193) d/dx (csc x) = -csc x cot x (page 193) d/dx (sec x) = Sec x tan x (page 193) d/dx (cot x) = -csc2 x (page 193) d/dx (C) = 0 (page 187) d/dx (xn) = nxn-1 Page 187 d/dx (ex) = ex Page 187 (cf)' = cf ' Page 187 (f+g) ' = f ' + g ' Page 187 (f-g) ' = f ' - g ' Page 187 (fg) ' = fg ' + f 'g Page 187 (f/g) ' = (gf ' - fg ') g2 Page 187 Lim sin x/ x = X-->0 1 Page 190 Lim (cos x -1)/x = x-->0 0 Page 192 Chain Rule If "g" is differentiable at "x" and "f" is differentiable at g(x), then the composite function F=f • g defined by F(x) = f(g(x)) is differentiable at "x" and F ' is given by the productF '(x) = f '(g(x)) • g '(x)In Leibniz notation' if y = f(u) and u = g(x) are both differentiable functions, thendy/dx = (dy/du)(du/dx) Page 197 Power Rule combined with the Chain Rule If "n" is any real number and u = g(x) is differentiable, then (d/dx)(un) = (nun-1)(du/dx) Alternatively (d/dx)(g(x))n = n(g(x))n-1 •g '(x) d/dx(sinh-1(x)) = Chapter 3 1 / ((1+x2)1/2) d/dx(cosh-1(x)) = Chapter 3 1 / ((x2-1)1/2) d/dx((tanh-1(x)) = Chapter 3 1 / (1-x2) d/dx(csch-1(x)) = Chapter 3 -1 / (|x|(x2+1)1/2) d/dx(sech-1(x)) = Chapter 3 -1 / (x(1-x2)1/2) d/dx(coth-1(x)) = Chapter 3 1 / (1-x2) Absolute maximum aka: global maximumA function "F" has an absolute or global maximum at "c" if F(c) >_ F(x) for all x in D, where D is the domain of F. The number F(c) is called the Maximum Value of F on D. Also called an extreme value. Absalute Minimum F has an absalute minimum at "c" if F(c) <_F(x) for all x in D and the number F(c) is called Minimum Value of F on D. Also called an extreme value. Local Maximum A function F has a Local Maximum (or relitive maximum) at "c" if F(c) >_F(x) when x is near c. [This means that F(c) >_ F(x) for all x in some open interval containing c]. Similary, F has a Local Minimum at c if F(c) <_ F(x) when x is near c. Extreme Value Theorem If F is continuouse on a closed interval [a,b], then F attains an absolute maximum value F(c) and an absalute mimimum value F(d) at some numbers c and d in [a,b]. AuthorMattyj1388 ID33033 Card SetCalculus 1A, College of the Desert, Chapters1-4.txt Descriptiongeneral info Updated2011-06-23T22:27:33Z Show Answers