Consider the following statements:1. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) both exist, then \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists.2. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists, then both \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) must exist.Which of the above statements is/are correct?

Consider the following statements:1. If \(\mathop {\lim }\limits_{{\rm

1.	Consider the following statements:1. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) both exist, then \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists.2. If \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} \left\{ {{\rm{f}}\left( {\rm{x}} \right){\rm{g}}\left( {\rm{x}} \right)} \right\}\) exists, then both \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{f}}\left( {\rm{x}} \right)\) and \(\mathop {\lim }\limits_{{\rm{x}} \to {\rm{a}}} {\rm{g}}\left( {\rm{x}} \right)\) must exist.Which of the above statements is/are correct?
A.	1 only
B.	2 only
C.	Both 1 and 2
D.	Neither 1 nor 2
Answer» B. 2 only

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