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What Are Common Mistakes Students Make When Finding Limits with Substitution?

When students try to find limits by using substitution, they often make some common mistakes. Here’s a simpler list of those pitfalls:

  1. Not Checking for Indeterminate Forms: Many students dive right into substitution without checking if they get tricky forms like 0/00/0 or /\infty/\infty. If they skip this step, they might not notice that they need to simplify first.

  2. Forgetting to Simplify: If they find an indeterminate form, it's really important to simplify the expression. Sometimes students forget to factor or cancel out common terms, which makes it harder to figure out the limit.

  3. Misunderstanding the Limit: Some students think that if they can just plug in the limit value, it’s always correct. They forget that the limit could approach different values from the left side and the right side.

  4. Skipping Steps: If students rush through the process, they can end up making mistakes. It's important to show each step carefully because this helps catch errors.

  5. Ignoring Continuity: Limits depend on whether the function is continuous at that point. If students ignore this, they might come to the wrong conclusion.

By being aware of these common mistakes, finding limits can be much easier!

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What Are Common Mistakes Students Make When Finding Limits with Substitution?

When students try to find limits by using substitution, they often make some common mistakes. Here’s a simpler list of those pitfalls:

  1. Not Checking for Indeterminate Forms: Many students dive right into substitution without checking if they get tricky forms like 0/00/0 or /\infty/\infty. If they skip this step, they might not notice that they need to simplify first.

  2. Forgetting to Simplify: If they find an indeterminate form, it's really important to simplify the expression. Sometimes students forget to factor or cancel out common terms, which makes it harder to figure out the limit.

  3. Misunderstanding the Limit: Some students think that if they can just plug in the limit value, it’s always correct. They forget that the limit could approach different values from the left side and the right side.

  4. Skipping Steps: If students rush through the process, they can end up making mistakes. It's important to show each step carefully because this helps catch errors.

  5. Ignoring Continuity: Limits depend on whether the function is continuous at that point. If students ignore this, they might come to the wrong conclusion.

By being aware of these common mistakes, finding limits can be much easier!

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