Honors Calculus Jeopardy

Integrals

100

Name two methods used to approximate the area under a curve.

Riemann Sums and Trapezoidal Approximations.

200

If a function is increasing, LRAM will be an:

Underestimate.

300

Name three methods used to find volume using integrals.

Washer method, cross-sections, and disc method.

400

The derivative of a function is 12x^3 + 6x^2 + 2x + 12. Find its integral.

3x^4 + 2x^3 + x^2 + 12x + C

500

Evaluate the following integral: ∫_pi/6^pi/2 -csc(x)cot(x)

-1.

Derivatives

100

State two other names derivatives are known by.

Slope and instantaneous rate of change

200

The derivative of a constant (e.g. 7) is what?

Zero (0).

300

Find the derivative of the following equation: 

3x^5 + 12x^3 + 21x + 70

15x^4 + 36x^2 + 21

400

Which rules would you use to find the following derivative:e^(3x) + (18x)/(6x^2)

Chain Rule and Quotient Rule

500

Find dy/dx for 4x^3 - 3y^2 = 6

dy/dx = (2x^2)/y

Limits

100

What are three ways to evaluate limits?

Algebraically, graphically, and with tables.

200

When does a limit not exist?

A limit DNE when it does not match from left and right.

300

When is L'Hopital's rule used to evaluate limits and how does it work?

It is used when the limit of a rational expression DNE so you find the derivative of the denominator and numerator and find the limit.

400

Evaluate the following limit:lim(x->3) (x^3 + 2x - 1)

32

500

Evaluate the following limit: lim(x->-3) [(3x^2 + 3x)/(x+3)]

Limit DNE.