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# Test 4 Prep MA 241

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This 4 page Study Guide was uploaded by Angel Santos on Monday March 7, 2016. The Study Guide belongs to MA 241 at Embry-Riddle Aeronautical University - Daytona Beach taught by Irene Mojica in Spring 2016. Since its upload, it has received 42 views. For similar materials see Calculus I in Mathematics (M) at Embry-Riddle Aeronautical University - Daytona Beach.

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Date Created: 03/07/16

Test 4 Prep MA 241 Calculus I Rules d Constant Function: dx c =0 x n−1 Power Rule: (¿¿n)=n x d =¿ dx d x ∗d (x ∗d Product Rule: dx [f(x)g x ]= f dx ( (x))g dx ( f(x)) (x)∗d (x∗d g f(x)− f g(x) Quotient Rule: d f ( )= dx dx dx [g]x ) g (x) d ' ' Chain Rule: f ( (x)) f ( (x))g (x) dx a>0: d (ax)=a lna Exponential Function Base dx Trigonometric Functions: x csc¿ d sin x)=cosx d (tan )=sec x ¿ dx dx d ¿ dx d (cosx)=−sin x d = cot x)=−csc x d (secx =sec xtan x dx dx dx Inverse Trigonometric Functions: Test 4 Prep MA 241 Calculus I Rules x −1 d −1 1 d −1 1 csc ¿ dx(sin x)= 1−x 2 dx tan x )= 1+x2 ¿ √ d ¿ dx d −1 −1 d −1 −1 d −1 1 (cos x = 2 =(cot x = 2 (sec x)= 2 dx √1−x dx 1+x dx x√x −1 Logarithmic Functions: d 1 (lnx)= dx x x loa ¿ ¿ d ¿ dx Test 4 Prep MA 241 Calculus I Linear Approximations AKA tangent line Approximation y−y 1m(x−x ) 1 Slope of tangent line f(a+ f '(a)(x−a) L(x)= f(a)+ f'a)(x−a ) 1. Find the linearization of f( )=√x+3 at a=1 use it to approximate √3.98 and √4.05 −1 ' 1 2 1 f ( ) 2 (x+3 ) = 2 x+3 √ ' 1 1 f ( ) = 4 2 √(3 ) f ( ) 1+3=2 √ L x = f 1)+ f(1)(x−1 ) 1 L x)=2+ 4(x−1 ) 1 7 L(x)= 4+ 4 Test 4 Prep MA 241 Calculus I Linear Approximations

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