Limits
Find the limit of (8-x^3)/(x^2-4) as x approaches 2
-3
How do you take the derivative of a quadratic function
nxn-1....
How do you take the integral of a quadratic function?
xn+1/(n+1)
What does CAN stand for?
Conditions
Analysis
Name (of theorem)
Describe the washer method of evaluating volume problems about an axis.
pi Sab R(x)^2 - r(x)^2 dx
Tip: Washers have holes in them
Find the limit of (cos(x)-1)/x^2 as x approaches 0
-0.5
Find the derivative of 4x^5-3x^(1/2)
20x^4-(3/2)x^(-1/2)
Find the integral of x^2+sqrt(x^3)
(1/3)x^3+(2.5)x^5/2
What does NUT stand for?
Noun
Unit
Time
Describe the disk method of evaluating volume problems about an axis.
pi Sab R(x)^2
What is the name of the theorem that lets you evaluate limits with indeterminate values?
L'Hospital's rule
Name each of the rules on how to solve a derivative
Product rule = f'g+fg'
quotient rule = (f'g+fg')/(g^2)
Chain rule = f'(g)*g'
exponential rule = a^x ln(a)
Logarithmic rule logax = 1/(x ln(a))
What does the integral of an acceleration graph give.
a Velocity
what does SISSY stand for?
Separate
Integrate
Solve for C
Solve for y
Describe how to take a volume by a shapes cross section.
The integral of area is volume so take the integral of the area of the shape perpendicular to the x/y-axis with the bounds decided by the functions that make up the base.
Which direction does Limitx->1- indicate?
It indicates a function approaching from the left
Find the derivative of the function y= csc^2(x)+cot^2(x)
y' = -4cos(x)/(sin^3(x))
John was riding his motorcycle across the road. His acceleration during the crossing is given by the function x^2+3, where x is the time in seconds. at 1 second he was going 10 meters per second. What equation represents is his distance traveled at 2 seconds.
(1/12)x4+ (3/2)x^2 + 6.5x
How many places do you need to round to?
To the third decimal place
The base of a solid formed by cross sections is a circle with a diameter of 4 with the square cross-sections being perpendicular to the x axis. Find the volume.
128/3
Find the limit of (sqrt(x^2 + 11)-6)/(x-5)
5/6
xe^y+1 = xy (use implicit differentiation)
dy/dx = (y-ey)/(x(ey-1))
Name the special rules for integration
Sum rule: S(f+g) dx = S(f)dx + S(g)dx
Difference rule: S(f-g) dx = S(f)dx - S(g)dx
Integration by parts: Suv dx = uSv dx - Su'(Sv dx) dx
What was Calculus made for?
Physics and other sciences describing the natural world.
A shape is made out of the functions y= x^2, x=4, and the x axis. What is the volume of the new shape formed when the shape is rotated about the x-axis?
243pi/5