This theorem states that, if the function k is a composition of two functions:
k(x) = f o g(x) = f[g(x)],
then its derivative can be formed by
i. differentiating f with respect to g(x) and
ii. multiplying by g’(x):
What is the Chain Rule?
100
The value f(x) that a function approaches as it approaches some value x.
What is a limit?
100
This is the definition of an integral.
What is the area under the curve?
100
d/dx sin(x)
What is cos(x)?
100
These two men are arguably the creators of calculus, for which there is a controversy named after them.
Who are Isaac Newton and Gottfried Leibniz?
200
If a function f is continuous on a closed interval [a,b] , then for every value k between f(a) and f(b) there is a value c between a and b such that f(c)=k
What is Intermediate Value theorem?
200
Limit of f of x as x approaches infinity (or negative infinity) is b
What is a horizontal asymptote?
200
∫ (x^2) dx
w/ upper bound=4 and lower bound=0
What is 64/3 or 21.3333?
200
This is the interpretation of what f'(x) is to f(x).
What is slope?
200
This country, aside from ancient Greece and European countries, is noted for its contribution to calculus, including the idea of infinity and infinite series.
What is India?
300
This theorem states that if f(x) is continuous on the closed interval [a,b], then f(x) has both a maximum and minimum.
What is Extrema Value Theorem?
300
lim (x^2-1)/(x-1)
x->1
What is 2?
300
∫ (x^3+2x^2-6x-100) dx
w/ upper bound=5 and lower bound=-1
What is 768?
300
d/dx tan(x)
What is sec^2x?
300
This name is another name for Calculus given by Newton
What is the science of fluents and fluxions.
400
The theorem states that the integral on [a,b] is
f(x) dx = F(b) - F(a).
What is the Fundamental Theorem of Calculus?
400
The term when either of the two limits of a function of a real variable x as x approaches a specified point either from the left or right of that function.
What is a one-sided limit?
400
∫6x^2 + 5x
What is 2x^3+(2.5)x^2+C
400
The term to describe that the left hand and right hand limits are the same at any given point of a graph.
What is differentiable?
400
This Greek mathematician was the first to find the tangent to a curve.
Who is Archimedes?
500
The theorem describes
f'(c) = (f'(b) - f'(a))
__________
(b - a)
What is Mean Value Theorem?
500
lim (sin x)/x
x->0
What is 0?
500
Type of integral first learned in class
What is numerical integral?
500
This is the quotient rule of derivatives.
What is d/dx(u/v)=(u'v-uv')/v^2
500
This mathematician developed both a special type of integral as well as the constant e.