LDFAoDIAoITetc

Limits

100

lim x->2   x^2

4

200

lim x->3   x^2-4

5

300

lim x->4   x^2+2/x

9/2

400

lim x->2   x^2-7/x-4

3/2

500

lim x->0   sqrt(x+49)-7/x

1/14

Derivatives

100

y=x^2

2x

200

y=2x+2

2

300

y=2x^2+5

4x

400

y=5x^3+21

15x^2

500

y=8x^5+35

40x^4

Applications of Derivatives

100

y=ln x^2

2/x

200

y=5^x

5^xln(5)

300

y=9*6^x

9*6^xln(6)

400

y=(x^e)^2

2ex^(2e-1)

500

y=3^(4+sin x)

3^(4+sin x)cos(x)ln(3)

Integrals

100

S sqrt(x)dx

2/3x^3/2+C

200

S 5e^x dx

5e^x+C

300

S2/0  (x^2+2x^3+3x^7)dx

320/3

400

S (3e^x+5/x+ln5)dx   

3e^x+5ln(|x|)+ln(5)x+C

500

S (x^5-3x^3)(1/x-6)dx

1/5x^5-x^6-x^3+9/2x^4+C

Misc.

100

derivative of y=4x+12

4

200

lim x->3   x^3+6

33

300

y=ln^5(x^3+2)

(15x^2ln^4(x^3+2))/x^3+2

400

S (x^5+3x-6)/sqrt(x) dx

2x^3/2+(2/11x)^11/2-12x^1/2+C

500

lim x->5   x^5+10x-24/x-3

3151/2