AP Calculus AB Jeopardy!

Limits

100

What is     lim_x-0(sin5x)/x       ?

                     5

200

What is the lim_x-π/2+tanx ?

    negative infinite

300

What value of k would make f(x) continues at x=0? 

f(x) = (sinx)/(2x)   when x ≠ 0

f(x) = k                 when x=0

    1/2

400

What is the lim_x->inf (log5x)/(x²+7) ?

                    zero

500

If lim_x->3f(x) = infinity 

then x=3 is a...

    vertical asymptote

Differentiation

100

What is the derivative of log₅(2x) ?

           (x* ln5 )^-1

200

Find the derivative of f(x)=ln(x³+3x²+7).

              (3x²+6x)/(x³+3x²+7)

300

Find dy/dx for the following function: x²y³+y²+3x=y.

                   (-3-2xy³)/(3x²y²+2y-1)

400

If f(x)=cosx and g(x)=sinx, 

what is the derivative of f(g(x)) ? 

                     -sin(sinx)cosx

500

Solve for d²y/dx² when y²=3x²+4x+y at the point (2,5).

           -.036

Anti-differentiation

100

Integrate F'(x)=3x²+6x.

What is x³+3x²+C?

200

_π/6∫^5π/6 csc²θ dθ

         2*3^1/2

300

Integrate  

             (ln⁶x) / x

  

 1/7(lnx)⁷ + C

400

Find the slope of the tangent to the circle

 x²+y²=25

at the point (3,-4) 

                             3/4

500

Integrate 1/(9+x²).

                1/3(arctan(x/3)) +C

Theorems

100

 ∫_a^bf(x)dx=?

F(b)-F(a)

200

The Mean Value Theorem can be applied to which of the following functions on the closed interval [−3,3][−3,3]?

a) f(x)=x^2/3                     b) f(x)=|x-1|

c) f(x)=(x-2)/(x-5)          d) f(x)=(x-5)/(x-2)

c) f(x)=(x-2)/(x-5)

300

Find a value c such that the conclusion of the mean value theorem is satisfied for f(x)=2x³+6x-2 on the interval [-2,2].

                    2/3^1/2    or   -2/3^1/2

400

What theorem guarantees that if f(x) is continuous on [a,b] there is a<c<b for every y: f(a)<y<f(b)? 

The Intermediate Value Theorem 

500

If n is a known positive integer, for what value of k is 

₁∫^kx^n-1dx = 1/n

         k=2^1/n

Applications

100

Find the area of the region bounded by f(x)=x²-3x-10 and g(x)=-x²+5x+14.

                      170.667

200

Find the average acceleration of a particle over the interval (0,50) given v(50)=80ft/sec and an initial velocity of 10 ft/sec. Include units in your answer.

                     7/5 ft/sec²  

300

The rate of change of radius r of a circle is 4 cm/s. Find the rate of change of Area A when r=2cm.

                           16π

400

The acceleration of a particle is given by the function a(t)=3t²+7. Find the position function of the particle given that its initial velocity is 10 m/sec and an initial height of 80m.

            s(t)=(t⁴/4)+3.5t²+10t+80

500

Find the volume of the solid generated by revolving the region bounded by y=x², the x-axis, and x=2 around the y-axis.

                        8π