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Created Date: 3/16/2008 2:13:01 PM
Extreme Value Theorem. If f ( x ) is continuous on the closed interval [ a , b ] then there exist numbers c and d so that, 1. a £ c , d £ b , 2. f ( c ) is the abs. max. in [ a , b ] , 3. f ( d ) is the abs. min. in [ a , b ] .
Differential Calculus finds Function .2/ from Function .1/. We recover the speedometer information from knowing the trip distance at all times. Integral Calculus goes the other way. The “integral” adds up small pieces, to get the total distance traveled. That integration brings back Function .1/.
Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 12/9/2022 7:11:52 AM
This Calculus Handbook was developed primarily through work with a number of AP Calculus classes, so it contains what most students need to prepare for the AP Calculus Exam (AB or BC)
Calculus Formulas. d + 1. Power Rules: x n = nx n − 1 xn and ∫ xn dx = + c dx n + 1. d. Product Rule: [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ g ' ( x ) + f ' ( x ) ⋅ g ( x ) dx. d ⎡ f x ⎤ g x f ' x f x ⋅ g ' x. Quotient Rule: ( ) ( ) ⋅ ( ) − ( ) ( ) dx ⎢ = ⎣ g ( ) x ⎥ ⎦ [ ( g x ) ]2.
Slope of line through P1 x1, y1 and P2 x2, y2 : y1 y2. m x2 x1. Point-slope equation of line through P1 x1, y1 with slope m: y1. x x1. Slope-intercept equation of line with slope m and y-intercept b: y mx.
Basic Properties and Formulas TEXAS UNIVERSITY CASA CENTER FOR ACADEMIC STUDENT ACHIEVEMENT
Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...
It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide. The complete textbook (PDF) is also available as a single file.