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Let's analyze the problem and evaluate the limits provided:

**Given limits:**
- \(\lim_{{x \to a}} f(x) = 0\)
- \(\lim_{{x \to a}} g(x) = 0\)
- \(\lim_{{x \to a}} h(x) = 1\)
- \(\lim_{{x \to a}} p(x) = \infty\)
- \(\lim_{{x \to a}} q(x) = \infty\)

**We need to classify the following limits:**

### (a) \(\lim_{{x \to a}} [f(x) - p(x)]\)
- As \(f(x) \to 0\) and \(p(x) \to \infty\), this results in the form \(0 - \infty\).
- A limit in the form \(0 - \infty\) is not indeterminate because subtracting any finite number (0) from \(\infty\) results in \(-\infty\).
- Thus, this limit evaluates to **\(-\infty\)**.

### (b) \(\lim_{{x \to a}} [p(x) - q(x)]\)
- Both \(p(x)\) and \(q(x)\) tend to \(\infty\), so this limit is in the form \(\infty - \infty\).
- The form \(\infty - \infty\) is indeterminate, as the actual behavior depends on how \(p(x)\) and \(q(x)\) approach infinity relative to each other.
- Thus, this limit is **indeterminate** (\(I\)).

### (c) \(\lim_{{x \to a}} [p(x) + q(x)]\)
- Both \(p(x)\) and \(q(x)\) tend to \(\infty\), so this limit is in the form \(\infty + \infty\).
- A limit in the form \(\infty + \infty\) is not indeterminate and will result in \(\infty\).
- Thus, this limit evaluates to **\(\infty\)** (\(INF\)).

### Final Answers:
- (a) \(-\infty\)
- (b) \(I\) (Indeterminate)
- (c) \(INF\) (\(\infty\))

Would you like more details or explanations on any part of this? Here are a few related questions to deepen your understanding:

1. What other types of indeterminate forms exist beyond \(\infty - \infty\)?
2. How do you apply L'Hôpital's rule to evaluate indeterminate limits like \(\infty - \infty\)?
3. Why is the form \(0 \cdot \infty\) considered indeterminate?
4. How does the behavior of \(p(x)\) and \(q(x)\) affect the outcome of the limit in (b)?
5. Can indeterminate forms always be resolved using algebraic manipulation?

**Tip:** When evaluating limits, always check if the form is indeterminate before applying advanced techniques like L'Hôpital's rule.

Given that lim(x → a) f(x) = 0, lim(x → a) g(x) = 0, lim(x → a) h(x) = 1, lim(x → a) p(x) = ∞, and lim(x → a) q(x) = ∞, determine which of the following limits are indeterminate forms: 
(a) lim(x → a) [f(x) - p(x)], 
(b) lim(x → a) [p(x) - q(x)], 
(c) lim(x → a) [p(x) + q(x)]. For indeterminate forms, mark 'I'. For positive infinity, use 'INF'. For negative infinity, use 'NINF'. For cases where the limit doesn't exist or can't be determined, mark 'D'.

Explore how to solve limits involving indeterminate forms like ∞ - ∞ and evaluate expressions that yield ∞ + ∞. This problem provides step-by-step analysis on handling limits, infinity forms, and classifying cases with 'INF' and 'I'. Ideal for Calculus I students.

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