Calculus Jeopardy

Limit Evaluation

100

Using direct substitution, evaluate the following integral.  lim  (2x²+4x-1)

             x->3

29

200

Evaluate the following limit evaluation 

lim  (x²-4/x-2)

x->2

4

300

Solve the following limit evaluation 

lim    [(√x)-2/x-4]

x->4

1/4

400

Evaluate 

lim  (3x²+5/2x²-x

x-> ∞

3/2

500

Evaluate the following (The 3x is included in the radical (√4x²+3x/2x-5)       

x->∞

1

Definite Integral

100

Find the area bounded by the curve of the square of a variable, the horizontal axis, and the vertical lines where the variable equals one and four.

21

200

Evaluate the total accumulated value of the product of a variable and the square root of the quantity one plus the square of that variable, as it ranges from zero to the square root of three.

7/3

300

Determine the net area under the curve of the sine of a variable over one full positive half-cycle, starting from zero and ending at pi.

2

400

Accumulate the rate of growth described by the constant e raised to the power of three times a variable, as the variable increases from zero to two.

1/3(e⁶-1)

500

Integrate the multiplicative inverse of a variable plus two, over the interval where the variable goes from negative one to three.

ln(5)

Average Value

100

Find the average value of the function f(x)=3x²+2x over the interval [1,3]

17

200

Find the average value of f(x)=5 over the interval [2,6]

5

300

Find the average value of f(x)=x over the interval [0,4]

2

400

Find the average value of f(x)=3x² over the interval [0,2]

4

500

During a 9-hour workday, the production rate of a factory t hours after the start of the shift is given by the function r(t)=5+3t items per hour. Find the average hourly production rate.

18.5

Slope of a Tangent Line

100

Find the slope at the given point on the equation (f(x) = 2x² - 5x + 1) at (x = 2)

3

200

Find the equation of the tangent line to the curve y= x³ at the point (2,8)

y-8=12(x-2)                  or            y=12x-16

300

Find the slope of the tangent line to the circle x²+y²=25 at the point (3,4)

-3/4

400

Find the slope of the tangent line to f(x)=1/x at x=1

0

500

Find the equation of the line tangent to the curve y= x²+3x at the point where x=2

y=7x-4

Absolute Maximum/Minimum Value

100

Find the absolute maximum and minimum values of f(x)= 2x³-15x²+36x

Absolute maximum is 28

Absolute minimum is 27

200

Find x values where there is an absolute maximum and minimum values of f(x)=x⁴-4x³ on the interval [-1,4]

Absolute maximum at x=-1

Absolute minimum at x=3

300

Find the absolute maximum and minimum values of f(x)=sin(x)+cos(x) on the interval [0,π]                 (Yes that is pie)

Absolute maximum is √2

Absolute minimum is -1

400

Find the absolute maximum and minimum values of f(x)=(x/x²+1) on the interval [0,3]

Absolute maximum is at 0.5

Absolute minimum is at 0

500

Find the absolute maximum and minimum values for f(x)=x^2/3 on the interval (-1,8)

Absolute maximum is 4

Absolute minimum is 0