Derivatives and Such
Theorems, Anyone?
Reached Your Limit?
Calculus Hodge Podge
Fast as Lightning
100
According to the definition, the derivative at a point is the limit of these.
What are difference quotients?
100
It states a^2 + b^2 = c^2.
What is the Pythagorean Theorem?
100
Have a 0/0 form? Use his rule.
Who is l'Hospital?
100
His notation uses differentials such as dy and dx to denote derivatives.
Who is Leibniz?
100
It is the derivative of sin(x).
What is cos(x)?
200
If the derivative of f(x) is identically 0, then f(x) must be this.
What is constant?
200
Some people call it the Sandwich Theorem. When it comes to limits, it is sure to be your main squeeze.
What is the Squeeze Theorem?
200
It is the limit as x approaches infinity of arctan(x).
What is Pi/2?
200
It is the function one differentiates to obtain 1/x.
What is ln(x) + constant?
200
It is the derivative of cosh(x).
What is sinh(x)?
300
The function f(x) = |x| is NOT differentiable at this point.
What is x = 0?
300
According to this theorem, a continuous function on [a,b] assumes both an absolute maximum and an absolute minimum on [a,b].
What is the Extreme Value Theorem (EVT)?
300
It is the limit of sin(x)/x as x approaches 0.
What is 1?
300
It is the rule one uses to differentiate a composition.
What is the Chain Rule?
300
It is the derivative of tan(x).
What is sec^2(x)?
400
It is the derivative of sin(cos(x)).
What is -cos(cos(x))sin(x)?
400
Roughly speaking, this theorem says that a continuous function cannot skip values.
What is the Intermediate Value Theorem (IVT)?
400
It is the limit of sin(7x)/sin(2x) as x approaches 0.
What is 7/2?
400
Its sign determines the concavity of a function.
What is the second derivative?
400
It is the derivative of ln(x^2+1).
What is 2x/(x^2+1)?
500
This differentiable function equals its own derivative and takes on the value 1 at x=0.
What is e^x, the natural exponential function?
500
His theorem states that critical points are the only possible locations of local extrema.
Who is Fermat?
500
It is the limit as x approaches infinity of ln(x)/x.
What is 0?
500
If the derivative of f(x) changes sign from + to - at c, then f(c) is one of these.
What is a local maximum?
500
It is the derivative of csc(x).
What is -csc(x)cot(x)?
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