P3 Flashcards
Types of mapping?
One-to-one, many-to-one, one-to-many
relationship between f(x) and f-1(x) in terms of domain and range?
f(x) domain = f-1(x) range
f-1(x) domain = f(x) range
Inverse function only exist for ______?
one-to-one function
sec x= _____
cosec x= ______
cot x= _____
1/cos x
1/sin x
1/tan x
Trigonometric identities?
sin^2x+cos^2x=1
1+cot^2x=cosec^2x
1+tan^2x=sec^2x
Trigonometry addition formulae?
sin(A±B)=sinAcosB±cosAsinB
cos(A±B)=cosAcosB-+sinAsinB
Double-angle formula
sin(2A)=2sinAcosA
cos(2A)=cos^2(A)-sin^2(A)=1-2sin^2(A)=2cos^2(A)-1
algorithm of ln?
lna+lnb=ln(ab)
lna-lnb=ln(a/b)
klna=ln(a^k)
ln(e^x)=e^(lnx)=x
Common differentiation:
x^n
sinx
cosx
e^x
a^x
lnx
nx^(n-1)
cosx
-sinx
e^x
a^(x)·lna
1/x
Differentiation Chain rule?
Used in composite function
整体导数✖️内部导数
Differentiation Product rule?
f(x)=uv
f’(x)=uv’+vu’
Differentiation quotient rule?
f(x)=u/v
f’(x)=(vu’-uv’)/v^2
Common Integration:
x^n
sinx
cosx
1/x
a^x
e^x
sec^2x
x^(n+1)/n+1
-cosx
sinx
ln|x|
(a^x)/lna
e^x
tanx
∫f’(ax+b)dx=?
1/af(ax+b)+c
Integration Reverse chain rule?
1) k∫[f(x)^n·f’(x)]dx=?
Try y=[f(x)]^n+1
2) k∫f’(x)/f(x)dx=?
Try y=ln[f(x)]