Calculus practice

Limits

100

lim as x approaches -3 of (3x+2)

-7

200

lim as x approaches -1 of (x^3-1)/(x-1)

1

300

lim as x approaches -1 of (2x^2-x-3)/x+1

-5

400

lim as x approaches 0 to the negative side of (x+1)/x

-infinity

500

lim as x approaches 3 to the positive side of x/(x^2-2x-3)

positive infinity

Derivatives

100

f(x)=x^3/5 +2

f'(x)=3/(5*5th root of (x^2))

200

f(x)=x^4/7

f'(x)=4/(7*7th root of (x^3))

300

f(x)=|2x+1|

f'(x)=(4x+2)/|2x+1|

400

f(x)=3x^2/3 /x^3+1

f'(x)=-7x^3+2 / 3rd root of x *(x^3+1)^2

500

f(x)=4x^3/4 *(3x^4-1)

f'(x)=(57*|x|*|x^3|-3)/4th root of x

Integrals

100

integral from 0 to 3 of (2x-1) dx

6

200

integral from 1 to 3 of 2x+3dx

14

300

integral from 1 to 2 of (1/x)dx

ln(2)

400

integral from 1 to e of 1/x dx

1

500

integral from 0 to pi of sina da

2

Theorems

100

Def of a derivative function

f'(x)=lim as h approaches 0 of f(x+h)-f(x) / h

200

Derivative Formula 1

d/dx k =0

300

Derivative Formula 2

d/dx (k*f(x))=k*f'(x)

400

derivative e formula

d/dx e^f(x)=e^f(x) *f'(x)

500

Tangent and normals

y-f(a)=f'(a)(x-a)

U-Substitution

100

integral of 2x / (x^2+5)^4 (dx)

-1/3(x^2+5)^3 +C

200

integral of 15x^6 times sqrt3x^5+5 dx

2(3x^5+5) sqrt 3x^5+5 /3 +C

300

sort of (x^3-2)^=4 *3x^2 dx

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

400

integral of 15x^2 sort 5x^3-2 dx

2(5x^3-2) sqrt 5x^3-2 / 3 +C

500

integral of 6x/(3x^2+2)^3 dx

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