B. Cal Flashcards

1
Q

Chain Rule

A

Let y = f(g(x)), then y’ = f’(g(x)) × g’(x)

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2
Q

Product Rule

A

d/dx(uv) = uv’+ vu’

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3
Q

Quotient Rule

A

d/dx(u/v) = (vu’ - uv’)/v²

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4
Q

Power Rule

A

If f(x) = x^n, then f’(x) = nx^(-1)

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5
Q

Limit of sin(x)

A

lim[sinx] = sin(c)
x->c

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6
Q

Limit of cosx

A

lim[cosx] = cos(c)
x->c

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7
Q

Limit property of sinx

A

lim[sinx/x] = 1
x->0

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8
Q

Limit property of cosine

A

lim[(cosx - 1)/x] = 0
x->0

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9
Q

Slope-Intercept Form of Line

A

y = mx + b

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10
Q

Limit of exponential function when base > 1, and raised to x

A

lim = +∞
x->+∞

lim =0
x-> -∞

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11
Q

Limit of exponential function when base > 1, and raised to -x

A

lim = +∞
x-> -∞

lim = 0
x-> +∞

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12
Q

Limit of exponential function when 0< base < 1, and raised to x

A

lim = 0
x->+∞

lim = +∞
x->-∞

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13
Q

Limit of exponential function when 0< base < 1, and raised to -x

A

lim = +∞
x->+∞

lim = 0
x->-∞

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14
Q

Limit of logarithm function when base > 1

A

lim = -∞
x->0 (right)

lim = +∞
x->+∞

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15
Q

Limit of logarithm function when
0 < base < 1

A

lim = +∞
x->0 (right)

lim = -∞
x->+∞

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