Limits
What is a limit?
When a function becomes "arbitrarily close to a single number as x approaches c from either side.
What is the integral expression for the volume of a solid?
V= ∫ A(x)dx, with intervals from a to b
What 4 rules for differentiation did we learn this year?
Power, Product, Quotient, and Chain Rule
What does the acronym "PVA" stand for?
Position, Velocity, Acceleration
What is equation should you write when a question ask you about continuity of a limit?
limx->c f(x) = limx->c+ f(x) = limx->c-
In terms of x, what is the integral expression for the area between two curves?
A= ∫ [f(x)-g(x)]dx, with intervals in respect to x values.
Which rule should you use for this?
f(x)=(6x2+7x)4
Chain Rule
Calculate ∫a(t)=?
v(t)
When does a limit not exist?
When the limit has any type of discontinuity. (When the limit on the left does not equal the limit on the right)
When finding the area on a plane with respect to x...
You subtract the bottom function from the top one.
Differentiate and Simplify
f(t)=(4t2−t)(t3−8t3+12)
20t4−132t3+24t2+96t−12
When a situation calls for a particle to be at rest, what do you do?
Find wherever v(t)=0
When a limit approaches infinity and the highest degree is in both the numerator and the denominator then...
the limit is the ratio of coefficients of the highest degree.
What is the washer methods integral expression?
V= π ∫ (R^2-r^2)dx, with the interval from a to b
Differentiate and Simplify
g(x)=6x2/2−x
24x−6x2/(2−x)2
When a problem asks for the total distance a particle travels between two points, what do you do?
You find the integral of |v(t)| between time a and time b.
Evaluate limx→∞ f(x)
f(x)=x3−2x+11/3−6x5
limx→∞ f(x)= 0/-6 = 0
The following are the dimensions of a rectangular prism wooden box. 9 inches in length, 2 inches in width, and 1 1/2 inches in height. Calculate the total cost of silver plating for the whole box.
The total cost of silver plating is $103.50.
Differentiate and Simplify
f(x)=(3√12x+sin2(3x))-1.
f'(x)=−(3√12x+sin2(3x))-2(4(12x)-2/3+6sin(3x)cos(3x))
What do you do when a situation requires you to determine if the particle's speed is growing or decreasing at a given time?
You'd want to see if the velocity and acceleration at that particular time have the same signs, which would indicate that they're both growing. The speed would slow down if they had different indications.