Types of Discontinuity

Function $f\left(x\right)=\cos \left(\frac{1}{x}\right)$ has oscillatory discontinuity at point $x=0$.

Function $f\left(x\right)=\sin \left(\frac{1}{x}\right)$ has oscillatory discontinuity at point $x=0$.

Define the oscillatory discontinuity with one example.

This is the graph of a function $h\left(x\right)$.

Find the $x$-value at which $h\left(x\right)$ has an isolated point discontinuity.

This is the graph of a function $h\left(x\right)$.

Find the $x$-value at which $h\left(x\right)$ has a isolated point discontinuity.

This is the graph of a function $f\left(x\right)$. Dashed lines represent asymptotes.

Select the $x$-value at which $f\left(x\right)$ has an isolated point discontinuity.

This is the graph of a function $h\left(x\right)$.

Find the $x$-value at which $h\left(x\right)$ has a isolated point discontinuity.

This is the graph of a function $h\left(x\right)$.

Find the $x$-value at which $h\left(x\right)$ has a missing point discontinuity.

This is the graph of a function $f\left(x\right)$. Dashed lines represent asymptotes.

Select the $x$-value at which $f\left(x\right)$ has a missing point discontinuity.

Let function $f\left(x\right)=\frac{\sin x}{x}$.

The function $f\left(x\right)$ has a missing point discontinuity at $x=0$.

Let function $f\left(x\right)=\frac{x^2-4}{\left(x-2\right)}$.

The function $f\left(x\right)$ has a missing point discontinuity at $x=a$. Find the value of $\text{'}a\text{'}$.

Define the missing point discontinuity with one example.

If [.] denotes the Greatest integer function, then $f\left(x\right)=[x{]}^2-\left[x^2\right]$ is discontinuous at

The function $f\left(x\right)=\frac{4-x^2}{4x-x^3}$ is :

Let $g\left(x\right)=\left\{\begin{array}{c}1-x;\\ x+2;\\ 4-x;\end{array}\right.\begin{array}{c}0\le x\le 1\\ 1<x<2\\ 2\le x\le 4\end{array}$, then the numbers of points where $g\left(g\left(x\right)\right)$ is discontinuous is

A point in the domain that cannot be filled in so that the resulting function is continuous is called

The function $f\left(x\right)=\frac{1}{x}$ is 

Find the points of discontinuity of the function $f$, where $f\left(x\right)=\left\{\begin{array}{ll}{x}^3-4x+1& \text{ if }x\le 2\\ 5x-2& \text{ if }x>2\end{array}\right.$.

Consider the piecewise function, $h\left(x\right)=\left\{\begin{array}{lll}{x}^3& ,& x\in (-\infty ,0]\\ \frac{24}{x}-1& ,& x\in (0,8]\\ (x-1)(x+3)& ,& x\in (8,\infty )\end{array}\right.$, find the value of $h\left(-4\right)$.

If $f\left(x\right)=\cot x$, is not continuous at $x=\frac{n\pi }{2}$ when