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The correct answers are (b) and not (a) or (c).
Let’s analyze each statement:
The limit involves two terms, and for the limit to exist, both terms must individually exist. Let’s check each term:
This limit also goes to infinity as x approaches 1 from the right.
Since both terms individually go to infinity, the sum also goes to infinity. Therefore, statement (a) is incorrect.
This statement is incorrect. As shown earlier, both limits go to positive infinity, not negative infinity.
So, the correct answers are (b) and not (a) or (c).