Limits when there is a sine function?

  • #1

Homework Statement



lim x-> ∞ xsin(1/x)

Homework Equations





The Attempt at a Solution



I know that this is an ∞.0 type limit but I can't figure out how to change the sin function.

Thank you
 

Answers and Replies

  • #2
vanhees71
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Hint
[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]
 
  • #3
Hint
[tex]x \sin(1/x)=\frac{\sin(1/x)}{1/x}.[/tex]

Ahh thank you! Then you use L'Hopitals Rule?
 
  • #4
34,904
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I wouldn't. This limit is related to this well-known limit
$$\lim_{t \to 0}\frac{sin(t)}{t}$$
 
  • #5
I wouldn't. This limit is related to this well-known limit
$$\lim_{t \to 0}\frac{sin(t)}{t}$$

What do you mean?
 
  • #6
74
6
Hint 2: Use a substitution, then figure out what the appropriate change in the limit would be.
 

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