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Found problems: 1

2007 Gheorghe Vranceanu, 4
Tags: real analysis , function , ftc , inverse function , primitivability , integral , newton-leibniz
Let $ F $ be the primitive of a continuous function $ f:\mathbb{R}\longrightarrow (0,\infty ), $ with $ F(0)=0. $ Determine for which values of $ \lambda \in (0,1) $ the function $ \left( F^{-1}\circ \lambda F \right)/\text{id.} $ has limit at $ 0, $ and calculate it.