Find the Limit of g(x)sinx as x Approaches 0: Homework Help & Equations

  • Thread starter Thread starter klarka
  • Start date Start date
  • Tags Tags
    Analysis Limit
klarka
Messages
2
Reaction score
0

Homework Statement


g(x) = 1 if x is rational, 0 if x is irrational.

Determine the limit, or prove it doesn't exist.

lim g(x)sinx
x->0

Homework Equations


The Attempt at a Solution


I said the limit is 0.

0 < |g(x)sinx| < |sinx|

lim |g(x)sinx|= 0
x->0
-|sinx| < g(x)sinx < sinx

lim g(x)sinx
x->0

The < are less than or equal. I can't figure out how to put them in correctly.
This was on my final and it's driving me crazy! I couldn't decided if the limit was 0 or didn't exist. If you could point out my mistakes I'd appreciate it!
 
Physics news on Phys.org
No mistake. The limit is 0. -|sin(x)|<=g(x)*sin(x)<=|sin(x)|. The outer terms go to zero as z->0 so g(x)*sin(x) must also go to zero.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Limit of 0^0: Evaluating x^sinx
Replies
19
Views
2K
Finding Limit as x-> 0 of sin and cos equation
Replies
6
Views
2K
Is the Limit of sqrt(x+sinx)ln(x) as x Approaches Zero Solvable?
Replies
8
Views
2K
Is x/sinx Equal to 1 as x Approaches 0?
Replies
11
Views
20K
Limit of sin(x)cos(x)/x as x approaches 0?
Replies
5
Views
20K
Evaluating Limits: x Approach 0 & Beyond
Replies
3
Views
1K
Evaluate Limit: limx→0 (sinx/x)=1?
Replies
13
Views
5K
Calculate the limit cos(x)/sin(x) when x approaches 0
Replies
12
Views
3K
Finding the Limit of Trig Functions: 2x/sin3x, x->0
Replies
2
Views
2K
Limit of Trigonometric f'n as x approaches 0
Replies
3
Views
4K

Hot Threads

Recent Insights

Back
Top