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Section 1

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e^0 =

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Calculus Math

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Date created

Mar 14, 2020

Cards (50)

Section 1

(50 cards)

e^0 =

Front

1

Back

S (secx) dx =

Front

ln |secx + tanx| + C

Back

cotx d/dx =

Front

-csc^2(x)

Back

S (sinx) dx =

Front

-cosx + c

Back

S (-cscxcotx) dx =

Front

cscx + C

Back

sinx d/dx =

Front

cosx

Back

Steps for separation of variable:

Front

1) change y' to dy/dx 2) separate all "X"s and "Y"s 3) integrate both sides 4) simplify to y=

Back

S 1/ [ (a^2 -u^2) ^1/2 ] du =

Front

arcsin u/a +C

Back

ln (1) =

Front

0

Back

tanx d/dx =

Front

sec^2(x)

Back

cosx d/dx =

Front

-sinx

Back

S 1/ [ u (u^2 - a^2) ^1/2 ] du =

Front

1/a arcsec |u|/a + C

Back

Steps to solve differential equations:

Front

1) find derivatives 2) plug them into the differential equ. 3) Simplify (if the 2 sides equal then its a solution)

Back

Finding concavity and points of inflection:

Front

1) f'(x) 2) f''(x) 3) set f''(x) = 0 4) test values (box) 5) determine concavity intervals pts. of inflection where concavity direction changes

Back

Steps for Rolle's Thm:

Front

1) f(a) = f(b) 2) is f(x) continuous at [a,b] ? 3) differentiable? 4) at least 1 critical point in [a,b] equals 0 when plugged into f'(x)

Back

1 + cot^2 =

Front

csc^2

Back

S (secxtanx) dx =

Front

secx + C

Back

sin^2 + cos^2 =

Front

1

Back

arc sin & arc tan =

Front

right half of unit circle

Back

Finding increasing and decreasing intervals:

Front

1) f'(x) 2) f'(x) = 0 to find CP 3) test values (box) 4) determine inc/dec intervals extrema at points where inc/dec intervals change direction

Back

Steps for 2nd Fundamental Thm of Calc:

Front

1) plug in the "b" of the interval (# above the integral {S} ) 2) simplify 3) multiply that by the derivative of the "b"

Back

S (cscx) dx =

Front

-ln |cscx + cotx| + C

Back

arc cos =

Front

top half of unit circle

Back

cscx d/dx =

Front

-cscxcotx

Back

Steps for Mean Value Thm:

Front

1) continuous and differentiable at [a,b] ? 2) msec = {f(b) - f(a)} / (b-a) change in y / change in x 3) mtan = msec

Back

sinx/cosx =

Front

tanx

Back

arcsin (point) =

Front

angle

Back

Indefinite Integrals:

Front

_____ + C look at "estimated" area of a curve

Back

S (sec^2{x}) dx =

Front

tanx + C

Back

S (cosx) dx =

Front

sinx + C

Back

e^x d/dx =

Front

e^x

Back

Definite Integrals:

Front

____ ] (interval A to B) look at "actual" area of a curve

Back

S (-sinx) dx =

Front

cosx + C

Back

S (e^x) dx =

Front

e^x + C

Back

S (cotx) du =

Front

ln |sinx| + C

Back

S 1/ [ a^2 + u^2] du =

Front

1/a arctan u/a + C

Back

S (-csc^2{x}) dx =

Front

cotx + C

Back

Steps for average value:

Front

1) take definite integral of equ. 2) multiply that answer by 1/(b-a)

Back

Steps to find critical point:

Front

1) find f'(x) 2) set f'(x) = 0 3) solve for x

Back

Completing the square formula:

Front

[ x^2 +/- bx + (b/2)^2 ] - (b/2)^2 + c

Back

sin (angle) =

Front

point

Back

ln x d/dx =

Front

1/x

Back

secx d/dx =

Front

secxtanx

Back

ln (e) =

Front

1

Back

S (1/x) dx =

Front

ln |x| + C

Back

S (cscxcotx) dx =

Front

-cscx + C

Back

1 + tan^2 =

Front

sec^2

Back

S (tanx) dx =

Front

-ln |cosx| +C

Back

cosx/sinx =

Front

cotx

Back

S (csc^2{x}) dx =

Front

-cotx + C

Back