Core 3 Flashcards by Matt Meynell

Q

Sin(A-B)

A

SinACosB-SinBCosA

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Q

Sin(A+B)

A

SinACosB+SinACosB

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Q

Cos(A-B)

A

CosACosB+SinASinB

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Q

Cos(A+B)

A

CosACosB-SinASinB

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Q

Tan(A+B)

A

(TanA+TanB) / 1-TanATanB

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Q

Tan(A-B)

A

(TanA-TanB) / 1+TanATanB

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Q

Sin2A

A

2SinACosA

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Q

Tan2A

A

(2TanA) / 1-Tan^2A

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Q

Cos2A

A

2Cos^2A-1

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Q

Cos2A

A

1-2sin^2A

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Q

Cos2A

A

Cos^2A-Sin^2A

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Q

What mapping is y=mx+c?

A

One to one

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Q

What mapping is y=x^2+1?

A

Many to one

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Q

What mapping is y=x^3?

A

One to one

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Q

What mapping is y=x^3+2x+1?

A

One to one

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Q

What is the quotient rule?

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A

dy/dx=(Vdu/dx)-(Udv/dx)V^2, with U always being the top of the fraction

Q

What is the product rule?

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A

dy/dx=(Vdu/dx)+(Udv/dx)

Q

What is the chain rule?

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A

dy/dx=(dy/dx) x (du/dx)

Q

What is the differential of y=Ln(ax+b)?

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A

dy/dx= a/ax+b

Q

What is the differential of y=Ln(ax)?

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A

dy/dx=1/x

Q

What is the differential of y=e^ax+b?

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A

dy/dx=ae^ax+b

Q

What is the differential of e^x?

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A

dy/dx=e^x

Q

What is the general form for exponentials?

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A

Ut=ar^t

Q

What is the differential of y=(ax+b)^n?

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A

dy/dx=an(ax+b)^n-1

What is the differential of y=ax^n?

dy/dx=nax^n-1

What is the integration of y=(ax+b)^n?

1/a(n+1) x (ax+b)^n+1 + c

What is the integration of e^x?

e^x + c

What is the integration of e^ax?

1/a x e^ax + c

What is the integration of 1/x?

Ln(x) + c

What is the differential of y=2Ln(x)

2/x

1/sinA

CosecA

1/CosA

SecA

CotA

1/TanA

CotA

CosA/SinA

Tan^2A + 1

Sec^2A

1 + Cos^2A

Cosec^2A