Calculus Final Jeopardy

Chapter 2

100

Find the limit of 

lim         x-6  

x->6     x²-36

What is 1/12

200

Find the limit of

lim          3x²+4x-1  

x->∞      2x²-5x-2

What is 3/2

300

Find the limit of 

lim          sin(10x) 

x->0            x

What is 10

400

A ball is tossed vertically into the air from ground level with an initial velocity of 10m/s. Its height (in meters) and time t (in seconds) is given by the function h(t)=10t-4.9t². Estimate the ball's instantaneous velocity at t=1.

What is .2 m/s

500

Find the limit as it approaches infinity.

lim            20x²-3x  

x->∞      3x⁵-4x²+5

What is 0

Chapter 3

100

Differentiate with respect to x.

y= 4x⁵+x

What is 20x⁴+1

200

Find f' (x) when f(x)=(4x³+2x²+8)(2x²-6x).

What is 40x⁴-80x³-36x²+32x-48

300

Find f''' (3) when f(x)=-2e^x-8x³.

What is -2e^x-48

400

Differentiate with respect to x.

y=       2    

        2x⁴-5

What is       16x³     

           4x⁸-20x⁴+25

500

A truck enters the offramp of a highway at t=0. Its position after t seconds is s(t)=25t-0.3t³m for 0<t<5. How fast is the truck moving at the moment it enters the offramp?

What is V(0)=25 m/s?

Chapter 4

100

Find the critical points.

f(x)=8x³-x²

What are x=0 and x=1/12

200

Find the intervals on which f is concave up or down. Find the points of inflection.

y=x³-6x²+4

What is (-∞, 2) concave down, (2, ∞) concave up, and p.o.i. @ x=2

300

Find the critical points.

f(x)=sinx+cos²x on [0, 2π]

What are x=π/2, x=3π/2, x=π/6, and x=5π/6

400

Use L'Hôpital's rule to evaluate 

lim               x³-8      

x->2         x⁴+2x-20

What is 6/17

500

Find the indefinite integral.

f(x)=9x+15x^-2

What is 

  9x²     -15x^-1 +c

2

Chapter 5

100

Estimate the area under the graph of f(x)=1+x² from x=-1 to x=2 using three rectangles and a right endpoint approximation.

What is 8

200

Estimate the area under the graph of f(x)=1+x² from x=-1 to x=2 using three rectangles and midpoint approximation.

What is 5.75

300

Evaluate the definite integral

32         

∫     x^-6/5dx

1

What is 2.5

400

Evaluate the definite integral using U substitution.

u=5x+4

du=5dx

∫(5x+4)⁵dx

What is     (5x+4)⁶    +c

                    30

500

Evaluate the definite integral using U substitution.

u=4x-1

du=4dx

∫x√(4x-1) dx

What is   (4x-1)^5/2 +   (4x-1)^3/2  +c

                40                24

Chapter 6

100

Find the area of the region enclosed by the graphs of f(x)=x²+2 and g(x)=2x.

What is 10.66

200

Find the area of the region bounded by x=y²-2 and x=y.

What is 4.5

300

Find the area of the region bounded by the intersections of the curves.

y=x²-1, y=7-x²

What is 21.3

400

Find the volume of the solid with a base enclosed by x+y=1 with cross sections perpendicular to the y-axis being semi circles.

What is .13

500

The region bounded by the graph of y=2x-x² and the x-axis is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a triangle with a height 3x the base. What is the volume of the solid?

What is 1.6