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

We found this answers

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

Discussion about this question


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.

removable discontinuity - My Math Forum

... a removable discontinuity at a a. if f(x) =sin(1/x) ... discontinuity at x=0? What if f(x)=xsin(1/x) ... f has a removable discontinuity at a. let g(x ...

Please help me to check the answers - My Math Forum

1. given the function f defined for all real numbers x by ... discontinuity at x=0? What if f(x)=xsin(1/x) ... x) =X sin(1/x) has a removable discontinuity at x=0 3.

Calc I Examples for Exam 1 - Seminole State College

The function f(x) = sin(1/x) has a non-removable ... (1/x) has a removable discontinuity at x = 0. ... illustrate graphically the satisfaction of the epsilon ...

Lecture 5 : Continuous Functions De nition 1 f a f x f a x ...

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

Discontinuous Functions - Math24.net

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.

SHOW MORE ....

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

x 0 xsin 1x 0 23. Given that x 1 6 ... cos x 1 x has a removable discontinuity at x 0 ... x x 1 x 0 and x 1 are not removable. 31. If F x f x g x h x , ...

a = 1. 6. removable 2 1. - Washington University in St. Louis

value of the function f at 1. Letter Number x 1 x 1 when x ... mine what value for f 0 would make f x continuous at x 0. ... Show that f x has a removable ...

5.3 Continuity of Rational Functions - St Charles College

Use a table and graph y f (x). The function has a discontinuity ... has a removable discontinuity at x 2 and a ... FUNCTION MODELS if x < 0 or x > 1 x if 0 ...

Infinite and removable discontinuity | Math IQ | Math ...

... x = 0, when drawn, we see that the function is ... a Removable Discontinuity ? A function f is ... x sin (1/x) has a removable discontinuity ...

calculus - Is there a function with a removable ...

... $ is said to have a removable discontinuity at a point $x_0 ... which has a removable discontinuity at $x_0$ for ... new function $\tilde{f}(x_0) = \lim_{x ...

Algebra Help - Brown University Mathematics Department

... asymptotes occur when a function approaches infinity at a specific value of x or y. If a function has ... our function f seems ... discontinuity at x = 0.

Discountinuities for Functions of One and Two Variables

... when one talks about a discontinuity for a function f(x) ... (1=x) has no limit at x = 0 and ... for x 6=0,sothat x= 0 is a \removable discontinuity" for g ...

Discontinuities - University of Denver

x2 1 x 1 You can see that this function has a discontinuity at x= 1 ... The function f(x) has the given graph. It has a jump discontinuity at x= 0.

2.2 The Limit Concept - NTHU

... limx→0xsin 1 x, (10) Let F(x) ... then f(x) has a removable discontinuity at 0. (4) ... continuous functions and f/g is continuous x whenever g(x) ...

Module 8 - Continuity - Texas Instruments

The function has a jump discontinuity at x = 0. ... The function is not continuous at x = 0 because x = 0 is not in the domain of the function. ... 1] x ...

continuity f x x/ x x > x < x P - Mathematics at Dartmouth

particular we cannot call x = 0 a discontinuity of f because it ... x→c f(x) = L exists, then c is called a removable ... that the function f(x) = 1/x has positive ...

Harvey Mudd College Math Tutorial: Continuity

Example The function f(x) = 8 >> >< >> >: x; x 0 x2; 0

How to determine a removable discontinuity of a rational ...

Determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x=4 of f ... of the function has a vertical ...

Continuity of functions - Intelligent Perception

Removable discontinuity. The function has a removable discontinuity at $x=a$ when $\lim\limits_ ... Example. $$f(x) = x\sin \frac{1}{x}$$ at $x=0$ Is it continuous at ...

What is a jump discontinuity of a graph? + Example

... /x# has a jump discontinuity at x = 0. To the left of x = 0 f(x) has a value of ... of Discontinuity (removable vs ... discontinuity of the function #f(x) = 1/x ...

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, ...

Discontinuity | MathCaptain.com - Online Math Help ...

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

when the function f(x) has a discontinuity at x0; ... To prove that some function F(x) has a limit, say C, at x = x0, ... (f) lim ˚!ˇ tan˚ ˇ ˚ (g) lim x!0 ln(1+x) x

How to Find Discontinuity | eHow

One would guess that any x other than zero has a discontinuity, ... the left side of x=0 will give a function value f(x) ... removable discontinuity or point ...

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

How to Locate the Discontinuities of a Function | eHow

How to Locate the Discontinuities of a Function. ... the function f(x) = 1/x has a discontinuity at x = 0. 4. Use the determined discontinuities to write the domain ...

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,