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math185-s23:mt1-review [2023/02/11 12:24] pzhou |
math185-s23:mt1-review [2023/02/15 23:06] (current) pzhou [Sample problems] |
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===== Sample problems ===== | ===== Sample problems ===== | ||
1. Some of the midterm questions will conceptual, for example like this | 1. Some of the midterm questions will conceptual, for example like this | ||
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* Why we cannot switch the order of limits? If we define the double sum as | * Why we cannot switch the order of limits? If we define the double sum as | ||
$$ \sum_{i=0}^\infty \sum_{j=0}^\infty a_{ij} := \lim_{n \to \infty} \lim_{m \to \infty} \sum_{i=0}^n \sum_{j=0}^m a_{ij} $$ | $$ \sum_{i=0}^\infty \sum_{j=0}^\infty a_{ij} := \lim_{n \to \infty} \lim_{m \to \infty} \sum_{i=0}^n \sum_{j=0}^m a_{ij} $$ |