2.1.44 Calculation of Limits

Condition: a. Find the limit: \ [\ lim _ {x \ rightarrow 0} \ ln (x+1) \ sin \ left (\ frac {1} {x} \ right) \] b. Use the determination of the limits to prove that if \ [\ lim _ {x \ rightarrow a^{-}} f (x) = l \ text {and} \ lim _ {x \ rishtarrow a^{-} f (x) = m \ text {,} l = m} l = m} l = m} l = m \ Text {. } \] C. Use the determination of the limits to prove that if \ [\ lim _ {x \ rightarrow \ infty} g (x) = \ infty \ text {and} \ lim _ \ rightarrow \ infty} = l \ text {, then}}}} \ lim _ {x \ rishtarrow \ infty} f (g (x)) = l \ text {. } \]