161-f11-sg2-10-06

161-f11-sg2-10-06 - Fall 2011 MA 16100 Study Guide Exam 2(1...

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Unformatted text preview: Fall 2011 MA 16100 Study Guide - Exam # 2 (1) Average rate of change of y = f ( x ) over the interval [ x 1 ,x 2 ] : Δ y Δ x = f ( x 2 )- f ( x 1 ) x 2- x 1 ; average velocity. Definition of derivative of y = f ( x ) at a : f ( a ) = lim h → f ( a + h )- f ( a ) h or, equivalently, f ( a ) = lim x → a f ( x )- f ( a ) x- a ; interpretation of derivative: f ( a ) = slope of tangent line the graph of y = f ( x ) at a velocity at time a (instantaneous) rate of change of f at a (2) Derivative as a function: f ( x ) = lim h → f ( x + h )- f ( x ) h ; differentiable functions (i.e., f ( x ) exists); higher order derivatives. (3) Differentiation Formulas ( 1 ) d ( c ) dx = 0 ( 2 ) d ( x n ) dx = nx n- 1 ( 3 ) d ( e x ) dx = e x ( 4 ) d (sin x ) dx = cos x ( 5 ) d (cos x ) dx =- sin x ( 6 ) d (tan x ) dx = sec 2 x ( 7 ) d (sec x ) dx = sec x tan x ( 8 ) d (csc x ) dx =- csc x cot x ( 9 ) d (cot x ) dx =- csc 2 x ( 10 ) d ( a x ) dx = a x (ln a ) ( 11 ) d (ln...
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161-f11-sg2-10-06 - Fall 2011 MA 16100 Study Guide Exam 2(1...

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