| Limits and Continuity | Derivatives | The Value Theorems | Integrals | Miscellaneous |
|---|---|---|---|---|
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What are the tools for looking at limits?
- Table wise (numerically)
- Graph wise (graphically) - Algebra/Calculus wise (Analytically) |
What is -Cos(x) ?
Derivative of -Sin(x)
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What is MVT?
This common abbreviation is used to denote the "Mean Value Theorem"
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What is Integration?
This mathematical process is used to calculate the area under a curve on a graph.
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What is the Unit Circle?
This commonly referenced chart is often used to convert from degrees to radians, or the other way around.
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When does a limit fail to exist?
Coming from different directions and not ending up in the same place- jump
asymptotic behavior oscillating behavior |
What is the product rule?
d/dx ((f)(g)) = (f)(g')+(g)(f')
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What is the Intermediate Value Theorem?
If f(x) is continuous on [a,b] and K is any number between f(a) and f(b) then there is at least one number c between a and b where f(c)=K
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-cos(x)−10cot(x)+c
∫sin(x)+10csc^2(x)dx
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what is the meaning of life, the universe, and everything?
the number 42
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What is the definition of a limit?
If f(x) comes arbitrarily closer to a single number L as x approaches c from either side, the limit of f(x) as x approaches c is L
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What is -(Csc(x))(Cot(x)) ?
Derivative of Csc(x)
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What is the Mean Value Theorem?
If f(x) is continuous on [a,b] and differentiable on (a,b) then there exists a number c on (a,b) such that
f'(c)= (f(b)-f(a))/(b-a) |
6sin(z)+4sin^(−1)(z)+c
∫6cos(z)+(4/(√1−z^2)) dz
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What is a coffin?
The person who buys me doesn't need me, the person who makes me doesn't want me, and the person who uses me can't appreciate me.
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What is the definition of continuity at a point?
- f(c) is defined
- limit of f(x) as x approaches c exists - The limit of f(x) as x approaches c equals f(c) |
What is The derivative of [arcsin u] ?
1/((1-u^2)^(1/2))
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What is the Extreme Value Theorem?
If a function f(x) is continuous on [a,b] then f(x) has both a maximum and minimum on [a,b]. If f(x) has an extreme on an open interval (a,b) then the extreme occurs at a critical point.
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What is 28.226?
Area enclosed between (4/6)x-4 and -3x^2+7
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nine.
If two's company and three's a crowd, what are four and five?
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What is continuous?
The graph of x^2 is everywhere ______.
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What is (18x^2)+(9)+((2(12x^2))(24x)) ?
d/dx (6x^3)+(9x)-(12) +((12x^2)^2)
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What is Rolle's Theorem?
This particular case is an extension of the Mean Value Theorem (MVT), and is used to show what happens when f(a)=f(b) in the MVT.
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what is 241.982?
the function x^3+3x^2+7 rotated around the x-axis and bounded by the line y=3 in the second quadrant.
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It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 10 people have guessed four fruits correctly.
In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly? |
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