Limits: Graphically and Analytically
Continuity and Differentiability
TV and Movie Quotes
Before and After
Determining Derivatives
Utilizing Tangent Lines
100
This is the result of the following limit:
lim_(x\rightarrow0^-)f(x)+lim_(x\rightarrow0^+)f(x)-lim_(x\rightarrow0)f(x)
What is DNE?
100
These are the x-values where the function is discontinuous as well as their types of discontinuities.
What is x = 0 (Jump Discontinuity) and x = 2 (Point Discontinuity)?
100
"Everything changed when the Fire Nation attacked."
What is Avatar: The Last Airbender?
100
A two-ingredient sandwich followed by a tasty ring-shaped pastry.
What is Peanut Butter and Jelly Doughnut?
100
This is the derivative of
f(x)=5x^3+6\root(3)(x)-4/x
What is
f(x)=15x^2+2x^(-2/3)+4x^-2?
100
This is the equation of the tangent line at x = 1 given the function
h(x)=5f(x)-3g(x)
What is
y+2=8(x-1)?
200
This is the result of the following limit:
3lim_(x\rightarrow-2)f(x)-5lim_(x\rightarrow1^+)f(x)
What is -11?
200
These are the x-values where the function is non-differentiable as well as their types of non-differentiability.
What is x = -4 (Cusp), x = -3 (Sharp Turn), x = 0 (Jump Discontinuity), and x = 3 (Jump Discontinuity)?
200
"Life is like a box of chocolates: you never know what you're gonna get."
What is Forrest Gump?
200
Golf short game practice area served up in the title of a Dr. Seuss book.
What is a Putting Green Eggs and Ham?
200
This is the derivative of
y=-7cos(x)+10sec(x)+cot(x)
What is
dy/dx=-7sin(x)+10sec(x)tan(x)-csc^2(x)?
200
These are the x-values on the closed interval [0, 2π] where the following function has an undefined slope of the tangent:
f(x)=tan(x)
What is
x=\pi/2 and x=(3\pi)/2?
300
This is the result of the following limit:
lim_(x\rightarrow3)(2x^2-18x+36)/(x-3)
What is
-6?
300
This is the type of discontinuity that occurs for the following function at x = 2:
f(x)=(x^2-9)/(x-2)
What is Infinite Discontinuity?
300
"I'm gonna be King of the Pirates!"
What is One Piece?
300
"Larger" than life animated tale from Roald Dahl served as a dessert that sounds like it should be for shoe menders.
What is James and the Giant Peach Cobbler?
300
This is the derivative of
y=-9x^4e^x
What is
dy/dx=-36x^3e^x-9x^4e^x?
300
This is the equation of the tangent line at x = 2 given the function
k(x)=(f(x)+7)/(4g(x))
What is
y-5/6=1/2(x-2)?
400
This is the result of the following limit:
lim_(x\rightarrow5)(\sqrt(x+4)-3)/(x-5)
What is
1/6?
400
These are the following functions that are not differentiable for certain values on the x-axis:
f(x)=x^(2/5), g(x)=3tan(x), h(x)=(x-4)^(3/2)
What is f(x) and g(x)?
400
"Never send a human to do a machine's job."
What is The Matrix?
400
Hemingway's book about an elderly guy trying to catch an echinoderm that looks like a giant pickle
What is the Old Man and the Sea Cucumber?
400
This is the simplified derivative of
g(x)=(6tan(x))/(4x-11)
What is
g'(x)=((24x-66)(sec^2(x))-24tan(x))/(4x-11)^2?
400
This is the exact x-value where the following functions have parallel tangents:
f(x)=8e^x and g(x)=16x-23
What is
x=ln(2)?
500
This is the result of the following limit:
lim_(x\rightarrow-\infty)(\sqrt(36x^2-7x+9))/(5x+11)
What is
-6/5?
500
This is the value of a that makes the following piecewise function continuous across all the reals:
f(x)={((4x^3+8x^2-60x)/(x^2-25) if x<3),(2a+2x if x>=3):}
What is
a=-7/3?
500
"I'm a peacock captain! You gotta let me fly on this one!"
What is The Other Guys?
500
Paul McCartney's Bond theme plays as Bruce Willis fights off bad guys at the Nakatomi Building.
What is Live and Let Die Hard?
500
This is the simplified second derivative of
y=\pie^xsin(x)
What is
dy/dx=2\pie^xcos(x)?
500
This is the equation of the tangent line at x = π/4 in Point-Slope Form given the function
f(x)=xsin(x)cos(x)
What is
y-\pi/8=1/2(x-\pi/4)