Calculus Jeopardy

Slippery Slope

100

d/dx x²

2x

200

d/dx x³+x-1

3x² + 1

300

d/dx (x^5)(sec(x))

(5x^4)(sec(x))+(x^5)(sec(x)tan(x))

400

d/dx (cos(x^5))^6

-(30x^4)(cos(x^5))^5)(sin(x^5))

500

log2(2x²)

(1/ln(2))(2/x)

Integreat!

100

∫ 3x dx

(3/2)(x^2) +C

200

∫ xcos(x^2) dx

(1/2)sin(x^2)+C

300

∫(x^5-6x+3) dx

((x^6)/6)-(3x²)+3x+C

400

∫((x^3)-(1/x^3))

(x^4)/4+(1/2x²)+C

500

∫sec^2(x) dx

tan(x)+C

A Slice of Pi

100

sin(0)

0

200

cos(π)

-1

300

tan(π)

0

400

tan(π/2)

undefined

500

cos(π/6)

√(3)/2

Calculus Rules!

100

Let f be continuous on [a,b] such that x is in a point in [a,b] Let F(x) = fnInt(f(t), t, a, x) F'(x) = f(x)

1st Fundamental Theorem of Calculus

200

Let f and F be continuous on [a,b] and let F be an antiderivative of f fnInt(f(x), x, a, b) = F(b) - F(a)

2nd Fundamental Theorem of Calculus

300

If f is continuous on [a,b], then f has both a global (absolute) maximum and minimum value on [a,b]

Extreme Value Theorem

400

∫udv = uv - ∫vdu

Integration by Parts

500

Let f be continuous on some closed interval [a,b]. If d is between f(a) and f(b), then there exists some c between a and b such that f(c) = d

Intermediate Value Theorem

Tigger's Functions

100

1/tan(x)

cot(x)

200

sin(x)/cos(x)

tan(x)

300

sin(2x)

2sin(x)cos(x)

400

1/csc(x)

sin(x)

500

1-(cos(x))²

(sin(x))²