MIT OpenCourseWare: Single Variable Calculus (Fall 2006) - Exam 4 Formulas, Study notes of Mathematics

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18.01 Single Variable Calculus

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Fall 2006

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The following formulas will be printed with Exam 4.

sin

2 x + cos

2 x = 1; sec

2 x = tan

2 x + 1

sin^2 x = 2

cos 2x; cos^2 x = 2

cos 2x

cos 2 x = cos^2 x − sin^2 x; sin 2 x = 2 sin x cos x

d d d 1 d 1

dx

tan x = sec

2 x; dx

sec x = sec x tan x; dx

tan

− 1 x = 1 + x^2

dx

sin

− 1 x = √ 1 − x^2

tan x dx = − ln(cos x) + c; sec x dx = ln(sec x + tan x) + c