Camille's Calculus Jeopardy

Limits

100

lim_x->3(2x²-4x+5)

11

200

lim_x->2[(x²-4)/(x-2)]

4

300

lim_x->4(3x-5)

7

400

lim_x->0(x²+5x)/x

5

500

lim_x->3(2x-6)/(x-3)

2

Integrals

100

f(x)=4. Find the integral of f(x)

4x+C

200

f(x)=3x². Find the integral of f(x).

x³+C

300

f(x)=2x+5. Find the integral of f(x).

x²+5x+C

400

f(x)=2. Find the integral of f(x) from x=1 to x=4.

6

500

f(x)=3x². Find the integral of f(x) from x=0 to x=2.

8

Average Value

100

Find the average value of f(x)=5 on the interval [1,4].

5

200

Find the average value of f(x)=6 on the interval [0,5]

6

300

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

2

400

The average value of f(x)=2x on the interval [0,3]

3

500

Average value of f(x)=2x+1 on the interval [0,2]

3

Tangent Lines

100

The equation of the tangent line at the point (2, 5) if the slope of the tangent line is m=3

y-5=3(x-2)

200

The equation of the tangent line to f(x)=x² at the point (3,9)

y-9=6(x-3)

300

The equation of the tangent line to f(x)=x²+4 at x=1

y-5=2(x-1)

400

The equation of the tangent line to f(x)=x²+3x at x=2

y-10=7(x-2)

500

The equation of the tangent line to f(x)=x²-6x at x=3

y+9=0(x-3) OR y+9=0 OR y=-9

Extrema

100

The relative minimum of f(x)=x²-4x+5

1

200

The relative maximum of f(x)=-x²+6x

9

300

Find the absolute minimum and maximum of f(x)=x²-2x on the closed interval [0,3]

Absolute Min=-1 (at x=1)

Absolute Max=3 (at x=3)

400

Absolute Max and absolute Min of f(x)=3x+2 on the closed interval [1,4]

Absolute Min=5 (at x=1)

Absolute Max=14 (at x=4)

500

Find relative max and min of f(x)=x³-3x

Max=2 (at x=-1)

Min=-2 (at x=1)