Continuity and Discontinuity
Limits: Graphically
Random Trivia
Limits: Analytically
Limits Involving Infinity
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 result of the following evaluation for the function below:
2lim_(x\rightarrow0)f(x)
What is DNE?
100
This is the most common atom in the universe.
What is hydrogen?
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?
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 result of the following evaluation for the function below:
lim_(x\rightarrow-4^+)f(x)+lim_(x\rightarrow2^-)f(x)
What is -3?
200
This term is used when a player scores three strokes under par on a single hole in golf.
What is an albatross?
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?
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 yes?
300
This is the result of the following evaluation for the function below:
f(-2)-3lim_(x\rightarrow4^+)f(x)
What is -9?
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?
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 1?
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 result of the following evaluation for the function below:
lim_(x\rightarrow2)f(g(x))
What is 2?
400
This Hollywood star / comedian (initials B.M.) plays himself in the 2009 horror comedy film Zombieland.
Who is Bill Murray?
400
This is the result of the following limit:
lim_(x\rightarrow0)(sin(3x)/(6x)+(4-4cos(x))/(x))
What is
9/2?
400
This is the result of the following limit:
lim_(x\rightarrow\infty)(x^16-9x^5+10x^2)/(e^x)
What is 0?
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 result of the following evaluation for the function below:
13/4lim_(x\rightarrow1^+)g(f(x))
What is
-13/2?
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?
500
This is the result of the following limit:
lim_(x\rightarrow0)((-3xcos(x)+5sin(6x))/(12x))
What is
9/4?
500
This is the result of the following limit:
lim_(x\rightarrow-\infty)(\sqrt(36x^2-7x+9))/(5x+11)
What is
-6/5?