Calculus Jeopardy

Derivatives

100

Definition of a Derivative

What is the slope of a graph at a single point

200

The Derivative of (6x²+6)⁴

What is 48x(6x²+6)³

4(6x²+6)³ Power Rule

48x(6x²+6)³ Chain Rule

300

Derivative of 3x²+6x+5

What is 6x+6

3x²+6x+5 Power rule

400

Technique used for when you have some form of an "x"  raised to another form of an "x"

What is Logarithmic Differentiation

500

Consider the position of a particle moving along the x-axis given by the function x(t)=3t⁴-8t³+6t²-2t, where t represents time in seconds. Is the velocity increasing or decreasing at the point x=2.

What is Velocity is Increasing

v(t) = (d/dt)x(t)

v(t) = 12t³-24t²+12t-2

v(2) = 22

a(t) = (d/dt)v(t)

a(t) = 36t² - 48t - 12

a(2) = 60

v(2) > 0; a(2) > 0

Velocity is Increasing

Limits

100

Definition of a Limit

What is what value the grah looks like it's approaching given an input

200

Lim (4x+1)/(x-2)

x --> 1

What is -5

Plug in -1 for all values of x

300

Lim (4x² - 4)/ln(x)

x --> 1

What is 8

Plug 1 for all values of "x"

You get indeterminate of (0/0)

Use L'hopitals rule and take the derviative of top and bottom

8x/(1/x) --> 8x²

= 5

400

When The graph is not approaching the same value from the left and right sides

What is the limit does not exist

500

A useful way for finding the limit of something when it's indeterminate

What is L'hopitals rule

Integral

100

Definition of an integral

What is a function of which given function is a derivative or what is the area under a curve

200

What is the integral of x² + 3x

What is ⅓x³ +1.5x² + C

Derivative of ⅓x³ +1.5x² + C makes x² + 3x

300

What is the integral of  Sin(3x) + 3x³ln(3) + 2xe^x²

What is -⅓cos(3x) + 9ln(3)x² + e^x² + C

Derivative of -⅓cos(3x) + 9ln(3)x² + e^x² + C makes Sin(3x) + 3x³ln(3) + 2xe^x²

400

Solve ∫³₁ (xe^x² - 10x)dx

(No graphing Calculator)

What is 4010.183

(0.5e^x² - 5x²)|³₁ 

= 0.5e⁹ - 45 - (0.5 - 5)

= 0.5e⁹ - 0.5e - 40

= 4010.183

500

If f(x) = 5x⁻¹ + 3x⁴ and g(x) = 8x² + 3, what is the integral of f(x)g(x) + f(x) from 5>x>-2 rounded to the nearest thousandth place?

(No Graphing Calculator)

What is 477,533.126

Integral of 40x + 20x⁻¹ + 42x⁶ + 12x⁴ from 5>x>-2

(20x² + 20ln|x| + 6x⁷ + 2.4x⁵)|⁵_-2 

= (500 + 20ln(5) + 468750 + 7500) - (80 + 20ln(2) - 768 - 76.8)

477533.126

Fun Facts Related to Calculus

100

Name one of the two calculus inventors

What is Isaac Newton or Gottfried Wilhelm Leibniz

200

What does "Calculus" mean in Latin?

What is Pebble/Small Pebble

300

What is the derivative of acceleration called (starts with J)?

What is Jerk

400

Who Invented the Integral Sign (∫)?

What is Gottfried Wilhelm Leibniz

500

Who is the best Calculus Teacher?

What is Ms. Hommowun!!!!!

Calc BC Stuff/Other Random Stuff

100

What is capital of Mongolia

Ulanbaataar

200

Who is the Calc BC Teacher in MHS?

What is Mr. Stutz

300

Solve ∫¹₀ (xe^x)dx

(Answer is Probably a Whole Number)

What is 1

xe^x - ∫e^x |¹₀

(xe^x - e^x)|¹₀

= (e - e) - (0 - 1)

=1

400

What is Micah Friedman's Website?

What is Loq.to

500

What are the first 5 numbers in Euler's Number?

What is 2.7182