# The function f(x)=xsin(1/x) has a discontinuity at x=0. Is it removable?

CONTINUOUS FUNCTIONS (6) ... Is the discontinuity at x = 0 removable? Yes, since lim x!0 xsin ⇣1 x ⌘ = 0. Proof. |f(x)0| = xsin ⇣1 x ⌘ |x| ! 0 as x ! 0. Then ... - Read more

... x 0 is called a removable discontinuity. ... the function. is continuous at x=x 0. ... The set of discontinuities is an F ... - Read more

## The function f(x)=xsin(1/x) has a discontinuity at x=0. Is it removable? resources

### Examples 6.5.6(b): - Seton Hall University

The function f(x) = x sin(1/x) is continuous everywhere except at x = 0, where it has a removable ... that this function has a removable discontinuity at x = 0.

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We say f(x) has a removable discontinuity at aif we can ... (1=x) x

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Discontinuous Functions ... The function f (x) has a discontinuity of the first kind at x = a if ... Show that the function has a removable discontinuity at x = 0.

If 0

### Re: Is the function y=1/x discontinuous? - Tech-Archive.net

... you are talking about the function f(x)=1/x, ... > f has a nonremovable discontinuity at x=0 but ... As opposed to x sin 1/x which has a removable discontinuity ...

### Solutions for Problems for Chapter 3. 1 x 2

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### What is a jump discontinuity of a graph? + Example

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### 1. Limits and Differentiation - Intmath

Find the limit as x approaches 0 of (sin\ x)/x ... (1/(x))=0 And similarly, lim_(x->+-oo)(1/ ... This function has a discontinuity at x = 1, ...

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Non removable discontinuity occurs at a point x = a when $\lim_ ... {x\rightarrow 0}f(x)$ = 0 and f(0) ... Hence the function has an infinite discontinuity at x = 5.

### 2. The Limit Concept - MSU Department of Physics and Astronomy

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### How to Find Discontinuity | eHow

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### Continuity and Discontinuity - Calculus Wiki 2010

Is the function $f(x)$ continuous at the point $x=0$? ... this function, $f(x)$, ... is it a jump, infinite, or removable discontinuity? 1. $f(x)$ = $1/x$ at $x$ = \$0 ...

### Extension Question - Oregon State University

According to Step 3, the function e(x)=sin(1/x) has no continuous extension at x=0. ... Is there a differentiable extension of the function f(x)=xsin(1/x) at x=0?

### 2.5 Continuity and 2.6 Tangent Lines and Their Slope

De nition: Slope of the Tangent Line Given a function f and a point x 0 in its domain, the slope of the tangent line at the point (x 0;f(x 0)) (or at x

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### Math 221-Midterm 1 Review Guide - Welcome | Department of ...

has a jump discontinuity at x = 0; xsin(1 x) ... x2 are discontinuous at x = 0(not removable). ... To nd the vertical asymptotes of a function f(x), ...

### 2.4 Limits and Continuity 1. 2. - JSU | Mathematical ...

• f(x) has a removable discontinuity at x=c if both ) ... Discuss the continuity of each function: 1. f(x) ... e x x f x x 0 1 0 ( ) 7. g(x)=xsinx 8. 1 ( ) 2 + = x ...

### Continuous Functions - University of Hawaii

Removable Discontinuity lim x!c f(x) = lim ... Rede ne the function f(x) = (xsin 1 x if x6= 0, 2 if x= 0 ... so that the function f(x) = 8 >< >: 1 if x>3,

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