Let F be the function defined, for all x in [a, b] and F is continuous on [a, b], differentiable on the open interval (a, b), and
F'(x) = f(x)
for all x in (a, b).
What is the Fundamental Theorem of Calculus?
200
Find the equation of the tangent line to
h(x) =1–(x^2) at (2,–3).
What is y=–4x+5.
200
∫ 1/(xLna)
What is Log(base a) x
200
This teacher was mentioned several times in the flop song DMF by Yung Einstunner and Spiral Ster.
Who is Mrs. Hubbard?
200
Integral of absolute value of velocity vs. time.
What is total distance traveled?
200
If a function f(x) is continuous on the closed interval [a, b], where a < b, and differentiable on the open interval (a, b), then there exists a point c in (a, b) such that
f'(c)= [f(b)-f(a)] / [b-a]
What is the mean value theorem?
300
find the derivative of
f(x)=x^(2/3)((x^(4/3))+(x^(1/3))+(x^(-5/3))
What is 2x+1-(1/x)
300
∫Lnx dx
What is x ln(x) - x + C
300
Yung Einstunner struggles with probability because he has not had this teacher.
Who is Mr. Iles?
300
Little Timmy throws his baseball super fast. After watching the baseball fly, he decides that the velocity can be modeled by the equation v=4x^3+5x^2+12. He finds that that the acceleration at t=2 is this.
What is 80?
300
A differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero
What is Rolle's theorem?
400
differentiate y=sin(2x)+(cos(2x))^2
What is -2((sin2x)^2)+2(cos(2x)^2)-2(sinxcosx)
400
∫ (x^2)/(x^3 + 3) dx
What is (1/3)(Ln x^3 + 3) + C
400
This teacher taught calculus last year, but teaches different subjects at West High this year.
Who is Mr. Kuemmel?
400
Big Bobby goes to an All-You-Can-Eat Buffet and consumes flapjacks at a rate modeled by the equation V(t)=x^6+x^3+8x where t is in hours. How many flapjacks did Big Bobby consume after 2 hours?
What is 38.28 flapjacks?
400
A theorem that states that "for each value between the least upper bound and greatest lower bound of a continuous function there is at least one point in its domain that the function maps to that value"
What is the intermediate value theorem?
500
differentiate y=(sin(7x+ln(5x)))^(1/2)
What is ((7x+1)cos(7x+ln(5x)))/(2x(sin(7x+ln(5x))^(1/2)))
500
∫ (2y)/(y^4+1)
What is tan^(-1) (y^2) + C
500
This teacher teaches the Japanese Stop Sign of Death.
Who is Mr. Moran?
500
Thumper rides his scooter in a fashion that can be modeled by the position equation s(t)= e^(3x-1) + 5x^3 where distance is in centimeters of Find Thumper's velocity at t = 2 sec
What is 505 cm/sec
500
Let f, g, and h be continuous functions defined at L where g(x) is less than f(x) is less than h(x) & lim x-> a g(x) = lim x->a h(x)=L Then lim x->a f(x) = L