calc

Limits

100

lim_x->2 (3x+1)

7

200

lim_x->0 sinx/x

1

300

lim_x->∞ (5x²+3)/(2x²-x)

5/2

400

lim _x->1 (5x³-1)/(x-1)

3

500

lim_x->0(e^x-e^-x-2x)/x³

0

Derivatives

100

Derivative of x²

2x

200

Derivative of e^3x

3e^3x

300

Derivative of ln⁡(x²+1)

2x/(x²+1)

400

Derivative of sin²(x)

2sin(x)cos(x)

500

find dy/dx if y=x^x

y(lnx+1)=x^x(lnx+1)

Integrals

100

∫2x dx

x²+C

200

 ∫e^x dx

e^x+C

300

∫1/x

ln|x|+C

400

∫sin(x)

-cos(x)+C

500

∫₀¹ 6x² dx

2

Mystery Problems

100

Solve for x: 2x+5=15

5

200

Evaluate 3²+4²

25

300

If f(x)=x²+2x, find f(3)

15

400

Find the slope of the line through (1,2) and (3,6)

2

500

Solve d/dx (x³-3x)=0

x=1,-1,0