Limit of x*sin(1/x) as x approaches Infinity | Calculus 1 Exercises

We show the limit of xsin(1/x) as x goes to infinity is equal to 1. This means x*sin(1/x) has a horizontal asymptote of y=1. We'll also mention the limit with x at negative infinity, which is found in the same way and is also equal to 1. To figure this all out, we'll give 1/x a different name, and see that we actually have a limit in the form sin(x)/x with x approaching 0, which is a fundamental trigonometric limit equal to 1! #Calculus1

What other horizontal asymptotes/limits at ∞ would you like to see?

Limit of x * sin (1/x) as x approaches 0:    • Limit of x*sin(1/x) as x approaches 0...  
Proof for Limit of sin(x)/x: (coming soon):

Calculus 1 playlist:    • Calculus 1  

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