Karteikarten
C3
Karten in diesem Stapel (24)
- 1Polynomial F(x) can be put in the form....when divided by Q(x)F(x)=Q(x) x divisor + remainder
- 2What is the domain and range of a function?Domain: possible x values of a function
Range: possible values of F(x) - 3What does FG(x) mean?G(x) is a value of x in F(x)
so plug G(x) into the x value of F(x) - 4What is ln(x)?the inverse of e^x
- 5F(ax) and aF(x)?F(ax) = horizontal stretch of 1/a
aF(x) = vertical stretch of a - 6Sec, cosec, cot?Sec = 1/cos
Cosec = 1/sin
Cot = 1/tan - 7Identities derived from sin2 + cos2 = 11 + tan2 = sec2
1 + cot2 = cosec2 - 8arcsin, arccos, arctanreflection in y=x
- 9Addition identities for sin?Sin(A±B) = sinAcosB ± cosAsinB
- 10Addition identities for cos?cos(A±B) = cosAcosB ∓ sinAsinB
- 11Addition identities for tan?tanA ± tanB
tan(A±B) = --------------------------------------- 1∓ tanAtanB - 12Double angle formula for sinsin2A = 2sinAcosA
- 13Double angle formula for coscos2A = cos²A - sin²A
= 2cos²A - 1
= 1 - 2sin²A - 14Double angle formula for tan2tanA
tan2A = 1 - tan²A - 15how do you work out R where Rcosx = a and Rsiny = bR = √(a² + b²)
- 16sinP + sinQ sinP - sinQ2 sin((P+Q)/2) cos ((P-Q)/2)
2 cos((P+Q)/2) sin((P-Q)/2) - 17cosP + cosQ cosP - cosQ2 cos((P+Q)/2) cos((P-Q)/2)
-2 sin((P+Q)/2) sin ((P-Q)/2) - 18chain rulen[F(x)]^n-1 x f'(x)
so differential of function multiplied by the differential of the function of a function as treated as y
dy/dx = dy/du x du/dx - 19product ruledy/dx = u(dv/dx) + v(du/dx)
differential of one times the other, plus the differential of the other times the original other - 20quotient rule u(x) v(x)[V(du/dx)-U(dv/dx)]
----------------------------
v²
differential of top times original bottom, minus differential of bottom times original top, all over original bottom squared - 21differential of e^xdy/dx = e^x
- 22differentiate ln(x)dy/dx = 1/x
- 23trigonometric differentialssinx → cosx
cosx → -sinx
tanx → sec²x
cosecx → -cosecx cotx
secx → secx tanx
cotx → -cosec²x - 24chain rule with trigsin(f(x)) → f'(x) cos(f(x))
cos(f(x)) → -f'(x) sin(f(x))
and so on...
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- GCSE maths Karteikarten am C3, erstellt von jonahberman am 24/05/2015.
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- jonahberman
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