Question: The function f : ( 0 , 1 ) R is differentiable, with bounded derivative. Must lim t 0 + f ( t ) exist

The function f:(0,1)R is differentiable, with bounded derivative. Must limt0+f(t) exist in R? Proof or counterexample.
The function f : ( 0 , 1 ) R is differentiable,

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