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memorize.aimemorize.ai (lvl 286)
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Section 1

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Restricted Domains for Inverse Trig. Functions

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Date created

Mar 1, 2020

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Section 1

(50 cards)

Restricted Domains for Inverse Trig. Functions

Front

arccos: [0,π] arcsin:[-π/2, π/2] arctan:(-π/2, π/2)

Back

lim (1 + x)^(1/x) x->0

Front

e

Back

∫tan u du

Front

-ln|cos u|+ c

Back

∫sec u du

Front

ln|sec u + tan u|+ c

Back

d/dx [a^u]

Front

(ln(a))(a^u)u'

Back

∫[f(u) + g(u)] du

Front

∫f(u) du + ∫g(u) du

Back

∫sin u du

Front

-cos u + c

Back

∫du/(u√((u^2) - (a^2)))

Front

(1/a)arcsec(|u|/a) + c

Back

∫u^n du

Front

((u^(n+1))/(n+1)) + c

Back

∫csc^2 u du

Front

-cot u + c

Back

∫sec^2 u du

Front

tan u + c

Back

d/dx [uv]

Front

uv'+vu'

Back

d/dx [cu]

Front

cu'

Back

d/dx [arcsec u]

Front

u'/(|u|√((u^2)-1))

Back

d/dx [tan u]

Front

(sec^2 u)u'

Back

d/dx [arccot u]

Front

-u'/(1+u^2)

Back

Unit Circle

Front

(cos, sin) *cos π/3 = 1/2, y cos π/6 = √(3)/2, x*

Back

∫du/u

Front

ln|u| + c

Back

∫a^u du

Front

(1/ln(a))a^u + c

Back

d/dx [u/v]

Front

(vu'-uv')/v^2

Back

d/dx [u^n]

Front

n(u^(n-1))u'

Back

d/dx [arcsin u]

Front

u'/ √(1-u^2)

Back

∫e^u du

Front

e^u + c

Back

∫csc u cot u du

Front

-csc u + c

Back

d/dx [x]

Front

1

Back

d/dx [arccos u]

Front

-u'/ √(1-u^2)

Back

Three ways a limit can fail to exist

Front

Different right and left behavior Unbounded behavior Infinite oscilation

Back

lim (sin x) / x x->0

Front

1

Back

d/dx [|u|]

Front

(u/|u|)u'

Back

∫cos u du

Front

sin u + c

Back

∫du

Front

u + c

Back

d/dx [csc u]

Front

-(csc u cot u)u'

Back

d/dx [arctan u]

Front

u'/(1+u^2)

Back

d/dx [u+v]

Front

u'+v'

Back

∫csc u du

Front

-ln|csc u + cot u|+ c

Back

∫sec u tan u du

Front

sec u + c

Back

d/dx [cos u]

Front

-(sin u)u'

Back

∫du/√((a^2) - (u^2))

Front

arcsin (u/a) + c

Back

∫cot u du

Front

ln|sin u|+ c

Back

d/dx [sin u]

Front

(cos u)u'

Back

∫du/((a^2) + (u^2))

Front

(1/a)arctan(u/a) + c

Back

d/dx [sec u]

Front

(sec u tan u)u'

Back

lim (1 - cos x) / x x->0

Front

0

Back

d/dx [arccsc u]

Front

-u'/(|u|√((u^2)-1))

Back

d/dx [loga(u)]

Front

u'/(ln(a)u)

Back

d/dx [cot u]

Front

-(csc^2 u)u'

Back

d/dx [c]

Front

0

Back

d/dx [ln(u)]

Front

u'/u

Back

d/dx [e^u]

Front

(e^u)u'

Back

∫kf(u) du

Front

k ∫f(u) du

Back