What Is Continuity?
Read this topicExplanations 4
- Take a look at the following two functions: We say that a function f(x)f(x)f(x) is continuous at a point x=ax = ax=a if f(x)f(x)f(x) is close to f(a)f(a)f(a) for all values of x…
By Matt Superdock, Japheth Wood, Cameron Montag, Toan Pham, Moor Xu
- It may be possible to test if a graph is continuous using limits, specifically two-sided limits. Here is a conjecture: Suppose we have a graph f(x)f(x)f(x) in which we want to t…
By Daniel Liu, Victoria Rodriguez, Moor Xu
- (Videos) Continuity and Limits Made Easy by PatrickJMT Here's a video by patrickJMT explaining what continuity is and the different types. A function is continuous if you can dr…
By Alex Federspiel
- (Video) Continuity on Piecewise Functions by PatrickJMT Here's a video by patrickJMT showing you how to figure out where a piecewise function is not continuous. While you can al…
By Alex Federspiel
Problems 6
- Define a function fff as follows. f(x)=0f(x) = 0f(x)=0 for all x≤0x \le 0x≤0. For all k∈Zk \in \mathbb{Z}k∈Z (integers), if x∈[2k,2k+1)x \in [2^k, 2^{k+1})x∈[2k,2k+1), then f(x)…
- At what points is the graph discontinuous?
- f(x)=∣x∣f(x)=|x|f(x)=∣x∣ continuous at x=0x=0x=0. Choose all facts that prove this statement is correct.
- What type of discontinuity is shown in the above graph?
- Which of the following functions is continuous everywhere?
- Where does this function have a discontinuity? f(x)=x+4x2+x−12f(x)=\frac{x+4}{x^2+x-12}f(x)=x2+x−12x+4