jeopardy

Integrals

100

Inegral from pi/4 to pi/2 of (2cos(x))dx

2-sqrt(2)

200

integral from pi/4 to pi/3 of (csc(x)cot(x))dx

-2sqrt(3)/3 +sqrt(2)

300

integral of x³e^x

x³e^x-3x²e^x+6xe^x-6e^x+c

400

 integral of 2x*e^5x

-1/2(3t+t²)cos(2t)+1/4(3+2t)sin(2t)+1/4cos(2t)+c

500

integral of x³*sinx

-x³cos(x)+3x²sin(x)+6xcos(x)-6sin(x)+c

limits

100

lim x--->oo 3x²+5x-3/4x²+20x-4

3/4

200

lim x--->0 e^x-x-1/cosx-1

-1

300

lim x-->8 2x²-17x+8/8-x

-15

400

lim x--->0 sin (x)-x/x³

-1/6

500

lim x-->-2 x³-x²-10x-8/5x³+12x²-2x-12

3/5

derivatives

100

d/dx(2x³-5x²+x-8)

6x²-10x+1

200

d/dx(x²+lnx-1/x+6)

2x+1/x+1/x²

300

f(x)=x²e^x f'(2)=?

8e²​​​​

400

d/dx(x³sin(pi*x))

3x²sin(pi*x)+pi*x³cos(pi*x)

500

f(x)=x²-4x/x³+1 f'(1)=?

5/4

combined math

100

f(x)=sin(3pi*x/4)  find f'(2)

0

200

lim x--->0 1-cos(x)/x²

1/2

300

integral of ln x

xln x-x+c

400

integral of -x²*cosx

-x²sin(x)-2xcos(x)+2sin(x)+c

500

f(x)=x²*cos(pi*x) f'(2)=?

4