Problem Teachers' Notes Hint Solution

Calculus Countdown

Game 1
P(x, x^2) = x^3
I(x^3) = x^4/4
P(x^4/4, 4) = x^4

Game 2
D(x^2) = 2x
R(2x) = 1/(2x)
P(1/(2x), x) = 0.5

Game3
I(x^2) = x^3/3

Also, D(ln(x)) = 1/x
R(1/x) = x
P(x, x) = x^2
I(x^2) = x^3/3

P(x^3/3, x^3/3) = x^6/9
R(4) = 1/4
P(1/4, x^6/9) =x^6/36

Game 4
D(D(D(ln(x))) = 2/x^3
R(x) = 1/x
P(1/x, 2/x^3) = 2/x^4
P(4, 2/x^4) = 8/x^4
D(8/x^4) = -32/x^5

Game 5
P(x^2, R(exp(x))) = x^2/exp(x)
D(x^2/exp(x)) = 2x/exp(x) - x^2/exp(x)
P(exp(x), last answer) = 2x-x^2