# Limit of (1+sin(4x))^(cot(x)) as x goes to 0+, L'Hospital's Rule | Summary and Q&A

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August 4, 2014
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Limit of (1+sin(4x))^(cot(x)) as x goes to 0+, L'Hospital's Rule

## TL;DR

This content discusses finding the limit of a complex function by using the properties of cotangent and Ln.

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### Q: What is the limit of the function as X approaches 0+?

The limit is positive infinity when X approaches 0+ and cotangent is involved.

### Q: How does introducing a new variable help in solving the problem?

Introducing a new variable allows the speaker to manipulate the equation and apply the Ln property, simplifying the problem.

### Q: What happens when the numerator and denominator both approach zero?

When both the numerator and denominator approach zero, the limit can be determined using l'Hôpital's rule.

### Q: How does the speaker simplify the cotangent function?

The speaker rewrites cotangent X as 1 over cotangent X, which allows for easier manipulation of the equation.

## Summary & Key Takeaways

• The speaker works through example number eight in section 4.4, finding the limit of a function as X approaches 0+.

• When X is approaching 0+ and cotangent is involved, the limit is positive infinity.

• To simplify the problem, the speaker introduces a new variable and uses the Ln property.

• By manipulating the equation and applying the Ln property, the speaker is able to simplify the problem further.