# Question #73434

##### 2 Answers

#### Explanation:

let

The red expression is a well known fundamental result.

Mar 16, 2017

# lim_(x to oo) x sin (1/x) = 1#

#### Explanation:

We want to find:

# lim_(x to oo) x sin (1/x) #

Let

And the limit can be rewritten, and evaluated;

# lim_(x to oo) x sin (1/x) = lim_(theta to 0) 1/theta sin theta#

# " " = lim_(theta to 0) (sin theta)/theta#

# " " = 1#

Where we used a fundamental trigonometry calculus limit:

# lim_(theta to 0) (sin theta)/theta =1 #