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Chapter 9: Problem 19

Find the limit. \(\lim _{x \rightarrow 0^{-}}\left(1+\frac{1}{x}\right)\)

Short Answer

Expert verified
The limit of the given function as \(x\) approaches \(0\) from the left side is \(-\infty\).

Step by step solution

01

Understand the Problem

The goal is to find the limit as \(x\) approaches \(0\) from the negative side of the function \(\left(1+\frac{1}{x}\right)\). This means we are interested in what happens to the function as \(x\) gets closer and closer to \(0\) from the negative side.
02

Substitution

Substitute \(x\) with a value very close to \(0\) but from the negative side in the function \(\left(1+\frac{1}{x}\right)\). For instance, consider \(x=-0.0001\). Substituting this value in the given function, it yields \(\left(1+\frac{1}{-0.0001}\right)\) = -9999.
03

Conclusion

In this case as \(x\) approaches \(0\) from the left side, the value of \(\left(1+\frac{1}{x}\right)\) tends to \(-\infty\).

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