Is it a correct sentence for apologizing?
" I'll do apologize for my impertinent and absurd attitude."

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I do apologize for my impertinent and absurd attitude.

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"I do apologize for my impertinent and absurd attitude."

"I do" not " I'll do"
If it is a spoken sentence, 'impertinent' is a bit formal and heavy word to use ,just use 'rude' instead.

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There is a confusion of tenses at the beginning ...

Either "I do .." or "I will .."