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Evaluate the numerator as x 0^-.
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Step-by-step solution
4 stepsTo evaluate the limit , we will analyze the behavior of the numerator and the denominator as approaches 0 from the left side.
Evaluate the numerator as .
As approaches 0 from the left, approaches .
Evaluate the denominator as .
The denominator is .
As approaches 0 from the left, will be a very small positive number (e.g., ). So, .
As approaches 0 from the left, approaches .Therefore, the denominator approaches , which is .
Combine the results for the numerator and denominator.
The limit becomes a negative number divided by a very small positive number.
Determine the final value of the limit.
When a negative number is divided by a very small positive number, the result tends to negative infinity.
The final answer is .
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