The Calculus Jeopardy @ PCI - Part III

Wrapped in Chains

100

The derivative of
f(x) = sqrt(121-x^2 

-x/sqrt(121-x^2)

200

The derivative of
f(x) = e^(2x^2) 

4xe^(2x^2)

300

The derivative of  
f(x) = pi^(3x) 

 3pi^(3x)ln(pi) 

400

The derivative of
f(x) =  ln (3x-x^2) 

 (3-2x)/(3x-x^2 

500

The derivative of
f(x) =  sqrt(ln x) 

1/(2xsqrtlnx)

To Trig or not to Trig

100

The derivative of
f(t) = sin 2t

2cos 2t

200

The derivative of
f(t) =  - cos 2t 

2sin 2t

300

The derivative of
f(t) =  -1/2tan t^2 

-tsec^2(t^2)

400

The derivative of
f(t) =  cos^2 (t) 

-2cos(t)sin(t)

500

The derivative of
f(x) =  sqrt sec(t) 

(tan tsect)/(2sqrtsect) or 1/2sin tsec^2t

Exponential

100

The value of a in  sqrt(x^(3)) =x^a 

3/2

200

The value of a in 8=2^a 

3

300

The value of a in x^2sqrtx=x^a 

5/2

400

The value of a in sqrtx/x^2 = x^a 

-3/2

500

The value of a in 8x^3=(2x)^a 

3

Antiderivative?

100

 int1/xdx 

lnx+c

200

 int(sqrtx) dx 

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

300

 int3cos(3x) dx 

sin(3x)+c

400

 intpix^2+7x dx 

pi/3x^3+7/2x^2+c

500

 int-csc^2(5x)dx 

 1/5cot(5x)+ C 

More Antiderivatives

100

 int8x+x^2dx 

x^2+x^3/3+c

200

 int2/(3x)dx 

2/3lnx+c

300

 intsqrtxdx 

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

400

 int2dx 

2x +c

500

 int(x+1)^2dx 

(x+1)^3/3+ c