Removable Discontinuity or Singularity
Read this topicExplanations 3
- Suppose f(x)f(x)f(x) is not continuous at x=ax=ax=a. There are a variety of ways this can happen; at least one of the conditions for continuity have to have been broken. This ty…
By Calvin Lee
- To envision a removable discontinuity, let us graph one: Let's graph the function f(x)=x−1x−1f(x) = \dfrac{x-1}{x-1}f(x)=x−1x−1. Now you might think: "Doesn't that function jus…
By Brandon Lin
- (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
Problems 9
- Where is the function f(x)=x2−4x+2f(x) = \frac{x^2 - 4}{x+2}f(x)=x+2x2−4 discontinuous?
- f(x)={x2−9x−3 if x≠35 if x=3f(x)=\left\{ \begin{array}{ll} \frac{x^2-9}{x-3} \;\text{ if }\; x \neq 3\\ 5 \;\text{ if }\; x = 3 \end{array} \right.f(x)={x−3x2−9 if x=35 if x=3…
- The function f(x)=x3−3x2−10x+24x−2f(x) = \frac{x^3 - 3x^2 - 10x + 24}{x-2}f(x)=x−2x3−3x2−10x+24 has a removable discontinuity at x=2x = 2x=2. Define a function ggg such that g(…
- Let fff and ggg be continuous functions. If g(c)=0g(c) = 0g(c)=0 for some c∈Rc \in \mathbb{R}c∈R and g(x)≠0g(x) \not= 0g(x)=0 for all x≠cx \not= cx=c, which of the following…
- Let fff and ggg be functions. If g(c)=0g(c) = 0g(c)=0 for some c∈Rc \in \mathbb{R}c∈R, will fgg\frac{fg}{g}gfg always have a removable discontinuity at ccc?
- Which of the following functions has a removable discontinuity?
- Which of the following functions has a removable discontinuity?
- Which of the following functions has a removable discontinuity?
- Which color line is continuous in the graph?