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## Homework Statement

a.) Let ##f,g:ℝ→ℝ## such that ##g(x)=sin x## and ##f(x)= \left\{

\begin{array}{ll}

x^2, x∈ℚ \\

0 , x∈ℝ\setminusℚ \\

\end{array}

\right. ##. Calculate ##\lim_{x \rightarrow 0} \frac{f(x)}{g(x)}##.

b.) Why l'Hospital rule cannot be applied here?

## The Attempt at a Solution

##\lim_{x \rightarrow 0} sinx=0##[/B]

**##\lim_{x \rightarrow 0} f(x)**

=\left\{\begin{array}{ll}

0, x∈ℚ \\

0 , x∈ℝ\setminusℚ \\

\end{array}

\right. ##

=\left\{\begin{array}{ll}

0, x∈ℚ \\

0 , x∈ℝ\setminusℚ \\

\end{array}

\right. ##

How to begin? I suppose I cannot apply l'Hospital.

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