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## Main Question or Discussion Point

Hi, I was studying for my upcoming calculus exam and couldn't be sure if I could solve this question:

[itex]\stackrel{lim}{x\rightarrow0}[/itex] x [[itex]\frac{1}{x}[/itex] ]

If x approaches 0 from left, then 0< x [[itex]\frac{1}{x}[/itex] ]<1

If x approaches 0 from right, then x [[itex]\frac{1}{x}[/itex] ]>1 since x [[itex]\frac{1}{x}[/itex] ]=[itex]\frac{x}{x-1}[/itex]

Hence, the limit is equal to 1.

Is this solution true? Thank you for any help :)

[itex]\stackrel{lim}{x\rightarrow0}[/itex] x [[itex]\frac{1}{x}[/itex] ]

If x approaches 0 from left, then 0< x [[itex]\frac{1}{x}[/itex] ]<1

If x approaches 0 from right, then x [[itex]\frac{1}{x}[/itex] ]>1 since x [[itex]\frac{1}{x}[/itex] ]=[itex]\frac{x}{x-1}[/itex]

Hence, the limit is equal to 1.

Is this solution true? Thank you for any help :)