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hint

1

sin (a+-b)

sin a cos a +- cos b sin b

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2

cos (a+b)

cos(a-b)

think opposite sign, cos cos sin sin

ex. for cos (a+b)

cos a cos b - sin a sin b

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3

how to find θ

θ=s/r

s = arc length

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4

BOBO - bigger on bottom 0

HA at y=0

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5

BETC - same degree

Ratio of leading coefficients = HA (y=ratio)

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6

BOTU - bigger on top

slant asymptote

leading coefficients + x’s on bottom and top, reduce x’s

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7

Vertical asymptotes in rational functions

factor left in the denominator = VA

if a hole occurs as well, the hole just occurs inside the VA.

VA takes precedence

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8

residual = actual - predicted (model)

pattern = NOT appropriate

Neg residual = overestimate

Pos residual = underestimate

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9

exponential growth

growing away from 0

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10

exponential decay

coming to 0

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11

exponentials

always inc or dec

end behavior → neg inf, pos inf, or 0, ONE SIDE will be 0

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12

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