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From the image you provided, it looks like you're working on a calculus assignment that involves analyzing limits and asymptotic behavior. Let me break down the relevant part of your question:

### Problem Context
- You are dealing with a function \( f(x) \) and are being asked to compute the **left-hand** and **right-hand limits** of \( f(x) \) as \( x \) approaches certain points \( \alpha \), where the function is undefined.
- You've already computed that there is a point where \( f(x) \) is undefined, and its location is provided as \( x = -\ln(5/16) \times (1/5) \).

### Task f: Left-hand and Right-hand Limits
You are asked to compute the following:
1. \( \lim_{x \to \alpha^-} f(x) = +\infty \)
2. \( \lim_{x \to \alpha^-} f(x) = -\infty \)
3. \( \lim_{x \to \alpha^+} f(x) = +\infty \)
4. \( \lim_{x \to \alpha^+} f(x) = -\infty \)

### Approach
1. **Identify the point \( \alpha \)**: In part (e), you calculated \( \alpha \), which is where the function is undefined, so you need to evaluate the behavior of the function as it approaches this point from both sides.

2. **Check the behavior of \( f(x) \) as \( x \) approaches \( \alpha \)**: Depending on how \( f(x) \) behaves near \( \alpha \), you need to determine if the limits tend to \( +\infty \) or \( -\infty \).

- For each limit (left-hand or right-hand), you can analyze the sign of the function and its behavior.

Would you like to walk through how to compute the left and right-hand limits, and analyze the sign changes around \( \alpha \)?

### Follow-up Questions
1. Do you want to break down the steps to analyze \( f(x) \) near \( \alpha \)?
2. Should we confirm the exact value of \( \alpha \) from your earlier steps?
3. Would you like help graphing the function to visualize the asymptotes?
4. Are there any additional questions on the previous sections of this problem?
5. Do you want to review any part of the limit concept before proceeding?

#### Tip:
For limits approaching infinity, especially near undefined points, always check how the numerator and denominator behave separately to see if the function diverges.

For the function f(x), analyze its behavior as x approaches a point where it is undefined. Specifically, compute left-hand and right-hand limits as x approaches this point, and determine if the limits go to +∞ or -∞. The given point is based on a natural logarithm expression and involves analyzing asymptotic behavior and limits.

In this calculus problem, explore how to calculate left-hand and right-hand limits for a function f(x) near a point where it is undefined, involving logarithmic expressions. Suitable for college-level students studying limits and asymptotic behavior.

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