Limits, Continuity, and Derivatives Flashcards

1
Q

Sin ϴ

A

Opposite/hypotenuse

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2
Q

Cos ϴ

A

Adjacent/hypotenuse

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3
Q

Tan ϴ

A

Opposite/adjacent

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4
Q

Csc ϴ

A

Hypotenuse/opposite

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5
Q

Sec ϴ

A

Hypotenuse/adjacent

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6
Q

Cot ϴ

A

Adjacent/opposite

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7
Q

1/2

A

Sin (30°) = Cos (60°)

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8
Q

Pythagorean

A

sin^2ϴ + cos^2ϴ = 1

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9
Q

Sin(2ϴ)

A

2sinϴcosϴ

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10
Q

Cos(2ϴ)

A

Cos^2ϴ - sin^2ϴ
1 - 2sin^2ϴ
2cos^2ϴ - 1

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11
Q

Tan^2ϴ

A

Sin^2ϴ/cos^2ϴ

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12
Q

Sum of cubes

A

a^3 + b^3 = (a+b)(a^2-ab+b^2)

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13
Q

Difference of cubes

A

a^3 - b^3 = (a-b)(a^2+ab+b^2)

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14
Q

Difference quotient

A

f(b) - f(a) / b-a

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15
Q

Instantaneous formula

A

f(t+h)-f(t)/h

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16
Q

Function

y=sin^-1x

A

y=sin^-1x

Domain
-1 ≤ x ≤ 1

Range
-π/2 ≤ y ≤ π/2

17
Q

Function

y=cos^-1x

A

y=cos^-1x

Domain
-1 ≤ x ≤ 1

Range
0 ≤ y ≤ π

18
Q

Function

y=tan^-1x

A

y=tan^-1x

Domain
-∞ < x < ∞

Range
-π/2 < y < π/2