AP Calculus

Limits

100

lim_x->3 (2x³-4x+7)

49

200

lim_x->oo ((10x⁶+4^x)/(2^x-4x⁵))

2

300

lim_x->1 ((x²+2x-3)/(x²-1))

2

400

lim_x->1((lnx)/(x-1))

1

500

lim_x->2 f(x)   f(x)= {x³-2    x<2

                            3x²-6   x>2

 6

Derivatives

100

d/dx(x⁴-2x³+3x+14)

4x³-6x²+3

200

d/dx(csc(x))

-csc(x)cot(x)

300

d/dx(sqrt(x)* 4e^x)

4e^xx^1/2+2e^xx-^1/2

400

d/dx((x²+3x-5)/(x²+2))

(-x⁴-6x³+15x²+4x+6)/(x³+2)²

500

d/dx(cos(e^x))

-sin(e^x)* e^x

Integrals

100

∫ 4x¹⁰ dx = ?

  4/11 x¹¹ +c

200

∫₀³ (9x-14)dx =?

-1.5

300

d/dx (∫_o^x(cos(t))dt) =?

cos(x)

400

Find average: f(x)=x²+2         [-1,2]

3

500

∫(x³cos(x⁴+2))dx = ?

1/4sin(x⁴+2)+c

Miscellaneous

100

v(t)=3cos(t²)   t(2)=6   Find p(7)

p(7)= 6.291

200

Find area between lines: [0,0.63]   y=2x²   y=sqrt(x)

0.167

300

Find volume of y=2x+1 rotated around x-axis  

between x=1 & x=4

367.566

400

Find the area under the curve using left hand intervals: 

x| 0 | 2  | 4  | 6 

y| 2 | 17 | 9 | 11 

L₃= ? 

L₃= 56

500

The graph y= x² has semi circles cross sections perpendicular to the x-axis. Find volume from x=0 to x=3 

76.341

Even more misc.?

100

∫₀^3pi/2 sin(t)dt =?

1

200

lim_x->a((x²-a²)/(x-a)) = ?

2a

300

Solve for x.

4*3^2x-5=32 

(5+log₃8)/2

400

d/dx(x²+y²=25) 

y'=-x/y

500

f(x)=2x²-6x+4     g(x)=f^-1(x)  Find g'(x) @ (2,1)

-1/2