Graphing indeterminate form functions

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For example, this limit: $$\lim_{x→0}(\frac{x}{{1-e}^{x}})$$

According to l'Hôpital's rule, it is an indeterminate form thus the solution of the above equation is -1.

However, when the function $$f(x)= \frac{x}{{1-e}^{x}}$$ is graphed, it appears to pass through the point (0,-1)as follows

The graph of f(x)

The problem is when x = 0 is substituted into f(x), it will give $\frac{0}{0}$ which is mathematically undefined.

But why does the graph have a solution to f(0)? Why does a graph have solution to indeterminate forms?

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By L’Hôpital’s Rule, the limit is: $$\displaystyle\lim_{x\to 0}\frac{x}{1-e^x}= \lim_{x\to 0}\frac{1}{-e^x}=-1.$$

Now, as you will see from the graph, both the Left and Right-Hand limits will approach -1 as x approaches 0. However, at x=0, the function is undefined. enter image description here