Find Two Paths of Approach from Which One Can Conclude $\left| \cos \left( \frac { 1 } { y } \right) \right| \leq 1$

question 385

Essay

Find two paths of approach from which one can conclude that the function has no limit as (x, y) approaches (0, 0).
-Does knowing that $\left| \cos \left( \frac { 1 } { y } \right) \right| \leq 1$ tell you anything about $( x , y ) \rightarrow ( 0,0 ) \sin ( x ) \cos \left( \frac { 1 } { y } \right)$ ? Give reasons for your answer.

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