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17 Cards in this Set
- Front
- Back
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lim(x→a) [f(x) + g(x)] =
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lim(x→a)f(x) + lim(x→a)g(x)
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lim(x→a) [c f(x)] =
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c lim(x→a) f(x)
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lim(x→a) [f(x) ÷ g(x)] =
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lim(x→a)f(x) ÷ lim(x→a)g(x)
if lim(x→a)g(x) ≠ 0 |
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lim(x→a) [f(x)]n =
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[ lim(x→a) f(x) ]^n
where n is a positive integer |
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The Squeeze Theorem
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If f(x) ≤ g(x) ≤ h(x)
when x is near a (except possibly at a) and lim(x→a) f(x) = lim(x→a) h(x) = L then lim(x→a) h(x) = L |
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(derivative of a constant function)
d/dx (c) = |
0
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d/dx (x) =
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1
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(power rule)
d/dx (x^n) = |
nx^(n-1)
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(the constant multiple rule)
d/dx [cf(x)] = |
c d/dx f(x)
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(the sum rule)
d/dx [f(x) + g(x)] = |
d/dx f(x) + d/dx g(x)
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(the difference rule)
d/dx [f(x) - g(x)] = |
d/dx f(x) - d/dx g(x)
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(the product rule)
d/dx [f(x)g(x)] = |
f(x) d/dx[ g(x)] + g(x) d/dx[ f(x)]
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(the quotient rule)
d/dx [f(x) / g(x)] = |
( g(x) d/dx[f(x)] - f(x) d/dx[g(x)] )
÷ [g(x)]^2 |
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(the chain rule)
F'(x) = |
f '(g(x)) • g'(x)
Leibniz notiation: dy/dx = (dy/du) (du/dx) |
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(the chain rule & power rule)
d/dx [g(x)]^n = |
n[g(x)]^(n-1) • g'(x)
Alternatively: d/dx [u^n] = nu^(n-1) du/dx |
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Formal Definition of a Derivative
The tangent line to the curve y=f(x) at the pointP(a, f(a)) is the line through P with the slope... |
m = lim(x→a) [(f(x) - f(a)] / [x - a]
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Formal Definition of a Derivative Using H
The tangent line to the curve y=f(x) at the pointP(a, f(a)) with (h = x - a) & (x = a + h) is the line through P with the slope... |
m = lim(h→0) [(f(a+h) - f(a)] / h
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