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| Formula for Population Growth/Decay |
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| Growth: Woe^(rt), Woe^(-λt) Decay: Woe^(-rt) |
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sin(A±B) = sinAcosB ± cosAsinB
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What is a function?
(rule) |
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| The rule that assigns each element "x" in the set "A" exactly ONE element "y" of set "B." |
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| cos(A±B) = cosAcosB ± sinAsinB |
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| cos2x = cos2x - sin2x = 1 - 2sin2x = 2cos2x - 1 |
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| The IMAGE of "x" under f: y=f(x) |
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| L'hopital's Rules can be applied when... |
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| Both functions are differentiable and both their limits are either equal to "0" or "∞" |
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| What IS L'hopital's rule? |
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| if both functions are differentiable and their limits are equal to 0 or ∞, then, their limits are also equal to their derivatives!! |
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L'hopital's Rule only works for...
(3 conditions) |
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- One sided limits
- x-->a where a can be a finite number OR ±∞
- Can be repeated as long as indeterminate forms exist!
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What is "set A" called? What is "set B" called?
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Set A = DOMAIN of f
Set B = COdomain of f |
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What about f(A) = ?
What is it called? |
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f(A) = y: y = f(x) for some xεA
"Range" |
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Define Composite Function
ex) fog |
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(fog)(x) = f[g(x)]
for each x in domain of g, for which g(x) is in the domain of f. |
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Define Polynomial function
(give its form) |
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f(x) = a° + a1x +a2x2 + ... + anxn
Where n is a non-negative number and an are real valued constants with an ≠ 0 |
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| rational function, give example |
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quotient of 2 polynomial functions
f(x) = p(x)/q(x), q(x) ≠ 0 |
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| f(x) = xr, r is real number |
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f(x) = ax
where a is POSITIVE constant other than 1, and the largest possible domain of f is xεR |
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Optimization Questions:
How to identify?
How to set up for solving? |
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"Find the biggest/smallest/largest.."
1. Draw a sketch
2. Introduce notations: let l be length, let Q be the maximized/minimized area - Label the diagram
3. Contruct equations that relate Q and other variables,
Q = f(x), domain
4. Find global extrema of f(x) |
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