What is the limit of sin|x|/x as x approaches 0?

  • Thread starter Thread starter math2010
  • Start date Start date
  • Tags Tags
    Limit
math2010
Messages
19
Reaction score
0

Homework Statement



I want to find the limit:

\lim_{x\to 0}\frac{sin|x|}{x}


The Attempt at a Solution



I know that the answer must be "limit doesn't exist" but I don't know how to arrive at that answer. I know that \lim_{x\to 0}\frac{sinx}{x}=1 but apparently it's a very different situation. Can anyone show me how to find this limit?
 
Physics news on Phys.org
Look at the two one-sided limits, and see if they are the same or different.
 
Mark44 said:
Look at the two one-sided limits, and see if they are the same or different.

What are the two one sided limits? That's what I don't get!
 
lim x -->0+
lim x -->0-

For the first, |x| = x
For the second, |x| = -x
 

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

##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
Replies
5
Views
2K
Calculate the limit cos(x)/sin(x) when x approaches 0
Replies
12
Views
3K
Limit and Integration of ##f_n (x)##
Replies
8
Views
2K
Find limit of multi variable function
Replies
10
Views
1K
Proving piecewise function is k-differentiable
Replies
5
Views
2K
Limit Definition of Derivative as n Approaches Infinity
Replies
20
Views
2K
How do you evaluate this limit?
Replies
8
Views
1K
What Are the Limits of Simple Functions as x Approaches Infinity?
Replies
7
Views
1K
Determine the limit of 2^x/x^2 as x approaches infinity....
Replies
26
Views
2K
Non-Differentiable Function proof
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top