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Universities » University of Texas (UT) » M - Mathematics » 408C - DIFFEREN AND INTEGRAL CAL.. » Flash Cards

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Class:M 408C - DIFFEREN AND INTEGRAL CALCULUS
Subject:Mathematics
University:University of Texas - Austin
Term:Fall 2010
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Types of discontinuity Jump removable infinite
(sin x)' cos x
(cos x)' -sin x
(tan x)' sec^2 x
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(csc x)' -csc x cot x
(sec x)' sec x tan x
(cot x) -csc^2 x
Integral (cos x dx) sin x + C
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Integral (sin x dx) - cos x + C
Integral (sec^2 x dx) tan x + C
Integral ( csc^2 x dx) -cot x + C
Integral ( sec x tan x dx) sec x + c
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Integral (csc x cot x dx) - csc x + C
Integral (tan x dx) ln |sec x| + C
Integral (cot x dx) ln |sin x| + C
Integral (sec x dx) ln |sec x + tan x| + C
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Integral (csc x dx) ln |csc x - cot x| + C
(sin ^-1 x)' one over the square root of (1 - x squared)
(tan ^-1 ) 1 / 1 + x^2
(sec ^-1 x)' 1 over |x| times square root of (x^2 - 1)
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integration by parts formula uv - Integral (v du)
sin (x + y) Indentity sin x cos y + cos x sin y
sin (x - y) Indentity sin x cos y - cos x sin y
cos (x + y ) Indentity cos x cos y - sin x sin y
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cos (x - y) Indentity cos x cos y + sin x sin y
tan (x + y) tan x + tan y -------------------- <- ( divison line) 1 - tan x tan y
tan (x - y) tan x - tan y --------------------------- <- division line 1 + tan x tan y
linear approximation f(a) + f(a)' (x-a)
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mean vaule thereom f(b) - f(a) ------------------- b - a
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 Types of discontinuity Jump
removable
infinite
 (sin x)'cos x
 (cos x)'-sin x
 (tan x)'sec^2 x
 (csc x)'-csc x cot x
 (sec x)'sec x tan x
 (cot x) -csc^2 x
 Integral (cos x dx)sin x + C
 Integral (sin x dx)- cos x + C
 Integral (sec^2 x dx)tan x + C
 Integral ( csc^2 x dx)-cot x + C
 Integral ( sec x tan x dx) sec x + c
 Integral (csc x cot x dx) - csc x + C
 Integral (tan x dx)ln |sec x| + C
 Integral (cot x dx) ln |sin x| + C
 Integral (sec x dx) ln |sec x + tan x| + C
 Integral (csc x dx)ln |csc x - cot x| + C
 (sin ^-1 x)'one over the square root of (1 - x squared)
 (tan ^-1 ) 1 / 1 + x^2
 (sec ^-1 x)'1 over |x| times square root of (x^2 - 1)
 integration by parts formulauv - Integral (v du)
 sin (x + y) Indentitysin x cos y + cos x sin y
 sin (x - y) Indentitysin x cos y - cos x sin y
 cos (x + y ) Indentitycos x cos y - sin x sin y
 cos (x - y) Indentitycos x cos y + sin x sin y
 tan (x + y) tan x + tan y
-------------------- <- ( divison line)
1 - tan x tan y
 tan (x - y) tan x - tan y
--------------------------- <- division line
1 + tan x tan y
 linear approximationf(a) + f(a)' (x-a)
 mean vaule thereom f(b) - f(a)
-------------------
b - a
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