Find Each of the Following Limits or Explain Why It $\lim _ { x \rightarrow \infty } \frac { \ln \left( a + b e ^ { x } \right) } { x }$

Find each of the following limits or explain why it does not exist.(a) $\lim _ { x \rightarrow \infty } \frac { \ln \left( a + b e ^ { x } \right) } { x }$ (b) $\lim _ { x \rightarrow \infty } x \sin \left( \frac { 1 } { x } \right)$ (c) $\lim _ { x \rightarrow 0 ^ { + } } \left( \frac { x } { 1 + x } \right) ^ { x }$

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