Limits
How we would write "the limit of f(x) as x approaches 4"
lim x->4 f(x)
Name two types of discontinuities
Removable, jump, endpoint, infinite, mixed
The derivative of x^3
3x^2
The equation for average rate of change
[f(x2)-f(x1)]/[x2-x1]
This movie was the sequel to Sam Raimi's Spider-Man
Spider-Man 2
How to spot a vertical asymptote
The limit gives a number divided by zero
The two conditions for a point on a function to be differentiable
It must be continuous
It must have a two-sided limit for its derivative
The limit equation used to find derivatives
lim h->0 [f(x+h)-f(x)]/h
A car travels 3 miles in 0.1 hours. What is its average rate of change?
The first feature length animated Disney movie
What is Snow White?
The limit of f(x) as x approaches 3
f(x)=(x^2-1-6)/(x-3)
5
The type of discontinuity at a vertical asymptote
Infinite
The derivative of 3/x^4
-12x^-5
Ms. B leaves a cup of tea out to cool. At one minute after pouring, the tea is 160 degrees Fahrenheit. At three minutes after pouring, the tea is 110 degrees Fahrenheit. What is the rate of change of the tea's temperature?
-25 degrees Fahrenheit/second
This holiday themed horror premiered four years before Halloween, and is considered by some to be the first slasher.
What is "Black Christmas?"
How to find a horizontal asymptote
Take the highest degree of the numerator and denominator
Find if the piecewise function is continuous at x=1
f(x)=x+2 when x < 1
f(x)=4x^2-x when x >= 1
Yes
The derivative of (x^3+2)*(x-3x) (you don't need to simplify)
(3x^2)(x-3x)+(x^3+2)(1-3)
A car's location is modeled by the function
d(t) = t^2 - 2t where t is in seconds and d(t) is in m.
What is the average speed of the car over 2 to 6 seconds?
6 m/s
Often considered Alfred Hitchcock's best movie, this thriller knocked Citizen Kane from the #1 spot in the 2012 edition of the Sight and Sound best movie poll
What is "Vertigo"
Find the limit as x approaches infinity for
(x^3+3x) / (x)
Infinity
Find if the piecewise function is differentiable at x = -4
f(x) = (1/2)x^2 when x<-4
f(x) = x^2 + 5x when x>=-4
No
The derivative of (x^3+2)/(x-1) (you do not need to simplify)
[(3x)(x-1)-(x^3+2)]/(x-1)^2
A car's location is modeled by the function
d(t) = t^2 - 2t where t is in seconds and d(t) is in m.
What is the car's instantaneous rate of change at t = 2 seconds?
2 m/s
This classic actor starred as the villain in Tim Burton's 1989 film "Batman"
Who is Jack Nicholson