Integrals
Name two methods used to approximate the area under a curve.
Riemann Sums and Trapezoidal Approximations.
Slope and instantaneous rate of change
What are three ways to evaluate limits?
Algebraically, graphically, and with tables.
If a function is increasing, LRAM will be an:
The derivative of a constant (e.g. 7) is what?
Zero (0).
When does a limit not exist?
A limit DNE when it does not match from left and right.
Name three methods used to find volume using integrals.
Washer method, cross-sections, and disc method.
Find the derivative of the following equation:
3x^5 + 12x^3 + 21x + 70
15x^4 + 36x^2 + 21
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.
The derivative of a function is 12x^3 + 6x^2 + 2x + 12. Find its integral.
3x^4 + 2x^3 + x^2 + 12x + C
Which rules would you use to find the following derivative:e^(3x) + (18x)/(6x^2)
Chain Rule and Quotient Rule
Evaluate the following limit:lim(x->3) (x^3 + 2x - 1)
32
Evaluate the following integral: ∫pi/6pi/2 -csc(x)cot(x)
-1.
Find dy/dx for 4x^3 - 3y^2 = 6
dy/dx = (2x^2)/y
Evaluate the following limit: lim(x->-3) [(3x^2 + 3x)/(x+3)]
Limit DNE.