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Consider the following statements:

1. If  and  both exist, then  exists.

2. If  exists, then both  and  must exist.

Which of the above statements is/are correct?

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  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

Answer (Detailed Solution Below)

Option 1 : 1 only
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Detailed Solution

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Concept:

Properties of Limits:

  • If  and  both exist, then  exists.
  • If  exists, then it’s not necessary  and  both exists.

 

Calculation:

We know that, if  and  both exist, then  exists.

Hence, statement (1) is correct.

We know that, If  exists, then it’s not necessary  and  both exists.

Hence, statement (2) is incorrect.

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