Compare and contrast continuity of a function?

javier007
Messages
2
Reaction score
0
PLEASE help me. I need to analyze the continuity of the piecewise function

f(x) = { sin(1/x) when x is not = to 0
_____{ 0_____ when x = 0

so i know sin(1/x) doent have a value at 0 but the second part of the function places the value of 0 at 0...BUT are both parts connected without any gaps, holes, or jumps in bewteen? in other words is it continuous or not?

I would appreciate it A LOT if you could explain it to me why or why not

thanks
 
Physics news on Phys.org
Do you know how to tell if a function is continuous at a point?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Can this function still be a constant function?
Replies
11
Views
1K
Uniform Continuity of functions
Replies
40
Views
4K
Is the given function continuous at x= 0? f(x) = {sin(1/x) if x≠0, 1
Replies
4
Views
4K
f(x) = 2x+1, proving that it is continuous when p = 1 with 𝛿 and ε
Replies
7
Views
1K
Medium Hard continuity proof Tutorial Q6
Replies
2
Views
1K
Proving piecewise function is k-differentiable
Replies
5
Views
2K
Why is this valid? Continuity of Functions Problem
Replies
3
Views
1K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
1K
Continuity of Function - f(x)=|cos(x)|
Replies
7
Views
2K
Show that this piecewise function is continuous at 0
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top