Parametric Equations
Limits: Analytically
Limits Involving Infinity
Continuity and Discontinuity
Delta-Epsilon Definition
Random Trivia
100
This is the Cartesian Form of the Parametric Equations
x(t)=2t+1 and y(t)=3\sqrt(t)
What is
y=3\sqrt((x-1)/2)?
100
This is the result of the following limit:
lim_(x\rightarrow3)(2x^2-18x+36)/(x-3)
What is
-6?
100
This is the result of the following limit:
lim_(x\rightarrow\infty)((4x^2-3)(5-x))/((x-3)(2x^2+5))
What is -2?
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
This is the value of δ (rounded to four decimal places) that satisfies ϵ = 0.02 for the following limit:
lim_(x\rightarrow4)(11x-3)=41
What is
\delta =0.0018?
100
This is the most common atom in the universe.
What is hydrogen?
200
This is the Cartesian Form of the Parametric Equations
x(t)=4log(t)-5 and y(t)=t^2
What is
y=(10^((x+5)/4))^2?
200
This is the result of the following limit:
lim_(x\rightarrow5)(\sqrt(x+4)-3)/(x-5)
What is
1/6?
200
This is the result of the following limit:
lim_(x\rightarrow-4^-)(3x)/(x+4)
What is
-\infty?
200
These are the intervals where the function is continuous.
What is
(-\infty,-2)\cup(-2,1)\cup(1,4)\cup(4,\infty)?
200
This is the value of δ (rounded to four decimal places) that satisfies ϵ = 0.005 for the following limit:
lim_(x\rightarrow5)(3/x+1/5)=4/5
What is
\delta =0.9587?
200
This term is used when a player scores three strokes under par on a single hole in golf.
What is an albatross?
300
This is the Cartesian Form of the Parametric Equations
x(t)=2cos(t) and y(t)=5sin(t)
What is
x^2/4+y^2/25=1?
300
This is the result of the following limit:
lim_(x\rightarrow7)(1/x-1/7)/(x-7)
What is
-1/49?
300
This is the result of the following limit:
lim_(x\rightarrow\-infty)(2^x+12)/(5+2^x)
What is
12/5?
300
This is the verdict on whether or not the piecewise function below is continuous at x = 0:
f(x)={(ln(x+1)+cos(x) if x<=0),(4e^(6x)+sin(\pix) if x>0):}
What is no?
300
This is the value of δ (rounded to four decimal places) that satisfies ϵ = 0.004 for the following limit:
lim_(x\rightarrow-2)(root(3)(3x-58))=-4
What is
\delta =0.0639?
300
This console serves as a platform for numerous games including Mario Kart 64, GoldenEye, and The Legend of Zelda: Ocarina of Time just to name a few.
What is Nintendo 64?
400
This is the Cartesian Form of the Parametric Equations
x(t)=8sec(t) and y(t)=7tan(t)
What is
x^2/64-y^2/49=1?
400
This is the result of the following limit:
lim_(x\rightarrow0)(sin(3x)/(6x)+(4-4cos(x))/(x))
What is
1/2?
400
This is the result of the following limit:
lim_(x\rightarrow\infty)(x^16-9x^5+10x^2)/(e^x+13x^7)
What is 0?
400
This is the verdict on whether or not the piecewise function below is continuous at x = 5:
f(x)={(|x-5|/(x-5) if x\ne5),(8 if x=5):}
What is no?
400
This is the value of δ in terms ϵ that proves the following limit:
lim_(x\rightarrow7)(sqrt(x+93)+4)=14
What is
\delta =10\epsilon?
400
This Hollywood star / comedian (initials B.M.) plays himself in the 2009 horror comedy film Zombieland.
Who is Bill Murray?
500
This is the Cartesian Form of the Parametric Equations
x(t)=cos(2t) and y(t)=sin(t)
What is
x=4-8y^2 or y=+-\sqrt(1/2-1/8x)?
500
This is the result of the following limit:
lim_(x\rightarrow0)((3xcos(x)+5sin(6x))/(12x))
What is
11/4?
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
These are the values of a and b that make the function continuous:
f(x)={(ax-b if x<1),(x^2 if 1<=x<5), (4b+2a-1 if x>=5):}
What is
a=5 and b=4?
500
This is the value of δ in terms ϵ that proves the following limit:
lim_(x\rightarrow1)(1/(x+3))=1/4
What is
\delta=12\epsilon?
500
This is the reverse order of Bending Styles that Aang masters throughout his journey to become the Avatar.
What are fire, earth, water and air?