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GWU - MATH 1232 - Study Guide - Midterm

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GWU - MATH 1232 - Study Guide - Midterm

School: George Washington University
Department: Math
Course: Single Variable Calc 2
Professor: Robinson
Term: Spring 2015
Tags: Calculus
Name: Calc 2 Study Guide
Description: A study guide for Midterm 1 with all of the formulas, how to find the inverse of a function, the derivative of an inverse, and other material.
Uploaded: 02/20/2018
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background image Calc 2 Exam One Study Guide This test is set to cover lectures one through 11, which goes over exponential functions, 
logarithmic functions, inverse trig functions, hyperbolic functions, indeterminate forms, 
l’hopital, integration by parts, trig integrals, trig substitution, integration by partial fractions, 
and the strategy for integration. To my knowledge, the last two topics have not been 
covered yet. 
Inverse Functions The chapter opens talking about one-to-one functions, which are functions that never
take the same value twice. A one-to-one function will pass the horizontal line test, 
meaning you can draw a horizontal line anywhere on the function and it will only 
intersect one point. 
A monotonic function is one whose slope is always positive or negative, and thus is 
always a one-to-one function
Notation o yf 1 ( x ) 1 f ( x ) o [ f ( x ) ] 1 = 1 f ( x ) o f 1 ( f ( x ) ) = x o f ( f 1 ( x ) ) = x) How to find an inverse o Replace f(x) with y in notation o Solve for x if possible o Switch x and y in the function  If f(x) is continuous on (a,b) then f -1 (x) is continuous on (f(a), f(b)) Derivatives of Inverse Functions f d dy ( ¿¿ 1()) d dx f 1 = 1 d dy () = 1 ¿ f 1' = 1 f ' f 1 ( x ) ) Exponents and logs Power o x a
background image Exponential o b x Rules: o a n *b n =(a*b) n o b n *b m =b n+m o a n b n =( a
b
) n o b n b m b nm o b -1 =1/b n o (b m ) n =b nm log 10 x n = nlog 10 x Derivatives of log functions  o d dx ( lnx ) = 1 x o u ln ¿ = 1
u
du dx d dx ¿ o d dx ( log b x)= 1 xlnb o d dx b x = b x ln b  INTEREST Geometric o A (t) =P(1+i/k) kt Exponential o A (0)= Pe it Doubling Time o N t = 2 t TD Derivatives  Trig o Sin(x)=cos(x) o Cos(x)=-sin(x) o Tan(x)=sec 2 (x) o Csc(x)=-csc(x)cot(x) o Sec(x)=sec(x)tan(x)

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School: George Washington University
Department: Math
Course: Single Variable Calc 2
Professor: Robinson
Term: Spring 2015
Tags: Calculus
Name: Calc 2 Study Guide
Description: A study guide for Midterm 1 with all of the formulas, how to find the inverse of a function, the derivative of an inverse, and other material.
Uploaded: 02/20/2018
4 Pages 40 Views 32 Unlocks
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