Limitless vs Unlimited

[Duc]

I have just taken an English tests.Here is one of its question.Put the correct form of the suggested word:

We should use solar energy because it's cheap,clean and .....(limit)
I put ''unlimited'' but my friend choose ''limitless''

As I looked up in the dictionary,they have the same meaning.Please explain their difference for me.
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Don't see your shade think you are great

[Mister Micawber]

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Frankly, I see no difference in their use here. 'Limitless', I think, would be the choice for 'infinite'.
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Native English teacher at Mister Micawber's

[Duc]

Thank you!However I'm very worried about my result
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Don't see your shade think you are great

[Mister Micawber]

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And you look worried!
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Native English teacher at Mister Micawber's