Calculus Final Project Jeopardy

Integrals

100

∫e^xdx

e^x+c

200

₁∫³ x²+3 dx

44/3

300

₀∫^∞ lnx dx

^∞

400

₀∫²√ (4-x²) dx

π

500

∫tanx^1/3 dx

1/√(3)(tan^-1)((2(tanx)^2/3-1)/(√(3)))+c

Derivatives

100

e^2x

2e^2x

200

x⁴+3x⁶

4x³+18x⁵

300

4sin⁴x

16sin³xcosx

400

Derivative of a sinx Macluarin Series Expansion

1-(3x²)/3!+(5x⁴)/5!-...

500

4x³y+y²=10

-12x²/(4x³+2y)

Limits

100

lim_x->0e^x

1

200

lim_x->25x²+3x⁴/7x⁴

68/56

300

lim_x->a(K)  

k

400

What is the lim_x->+infinity(1+1/x)^x  

e

500

lim_x->0sinx/x

1

Hyperbolics

100

Derivative of coshx

sinhx

200

Derivative of sechx

-sechxtanhx

300

Derivative of sinhx/coshx

sec²hx

400

∫cothu du

ln(sinhu)+c

500

Derivative of (e^x-e^-x)/2

coshx

General Calc

100

What's the area under a curve called?

Integral

200

What derivative rule do you use? g(f(x))

Chain Rule

300

Whats the derivative of an Inverse?

1/f^'(f^-1(x))

400

What a Taylor Series Called Centered at X=0

Macluarin Series

500

What is an infinite sum of widths of a function called?

Integral