AP Calculus AB Jeopardy

Limits

100

If f(x)=(x²+1)/x

lim_x>2f(x)

5/2

200

Evaluate lim_x->infinity (x^6 )/(9^x)

0

300

Given f(x)=(x²+2x-3)/(9x⁶+4x⁵+15x²) what is the limit of f(x) as x approaches infinity?

Limit of f(x) is 0.

400

Evaluate the following limit

lim_x->0 sinx² / (xtanx)

1

500

lim_x>0(1-cos(2x))/(xsin(3x))

2/3

Derivatives

100

If f(x) = 5x^(5/3) + (2/3)x^(9/4) - (1/2)x^(1/2),

then f^'(x) =

f'(x) = (25/3)x^(2/3) + (3/2)x^(5/4) -1/(4√x))

200

If f(x)=sin(x/3), find the tangent line at x=π

y-(√(3)/2) = (1/6)(x-π)

300

If f(x) = (2x² - 4x +3)(-5x³ +6x),

then f'(x)=

f'(x)= -50x⁴ +80x³ -9x² -48x +18

400

If f(x)= (x² +3x +2)/(x+3), (1) find the equation of the tangent line at x=1, and (2) use the tangent line equation to approximate f(1.01). For part 2, you can use a calculator, and round to the nearest thousandth.

1) y-(3/2)=(7/8)(x-1)

2) f(1.01)=1.509

500

If f(x)= (sin(1/(2x+1))) / (5x²+1), then f'(x)=

((-2cos(1/(2x+1))*(5x²+1))-10xsin(1/(2x+1))) / ((2x+1)² *(5x²+1)²)

Application of integrals

100

Find the volume if a region enclosing y=x-1, y=0, and x=3, is rotated about the line x=3. (You can use a calculator).

8π/3

200

What is the area of a region enclosed by the graphs y=-x²+4x+6 and y=-1.5x+6. You can use a calculator, and round to the nearest thousandth. 

27.729

300

Find the area of the region bounded by y=2x+5, and y=x²+2x+1 (No calculator) 

32/3

400

Find the volume of a solid whose base is bounded by the graphs y=x³, the y-axis, and x=1. Find the volume of a solid with a semi-circle cross section perpendicular to the y-axis. You can use your calculator, and round to the nearest thousandth.

0.039

500

Determine the volume of the solid obtained by rotating the region bounded by y=2√(x-1) and y=x-1 about the line x=-1 . (No Calculator)

96π/5

Integrals

100

When is a Left Riemann Sum an overestimate?

When the function is decreasing. 

200

Approximate the Left Riemann Sum using 4 su intervals given the following points: (1,3), (2,4), (5, 12), (7, 16), (10,22).

87

300

Write the integral of 3x²+5 from 4 to 6 in summation notation.

lim_n->infinity Σⁿ_i=1 (3(4+2i/n)²+5)(6/n)

400

Find the general antiderivative of x²e^{x^3}cose^{x^3}

(sine^{x^3})/3 + C

500

Find the general anti derivative of cos²x. (Hint: Review trigonometric identities)

(sin(2x))/4 + x/2

???

100

If the equation of a car's position(meters) over time(seconds) is represented by p(t)=6x+cos(2t), find the velocity at time t=3.(calculator permitted).

5.79 meters per second.

200

Given v(t)= -4+(t³+5t)²+24t and p(0)=7, find p(2).(calculator permitted)

p(2)=195.952 

300

Find the average value of f(x)=3x⁴-4× on interval [0,2].

5.6

400

Differentiate ( y³-1)/(2x²)=6 and find y' at(3,2)

y'=7/18

500

Find the solution to dy/dx=(4x²-√(5x))/12y if y(0)=16

√((4/3x³-2/15(5x)^3/2+16)/6)