### All High School Math Resources

## Example Questions

### Example Question #3 : Calculus I — Derivatives

Calculate .

**Possible Answers:**

The limit does not exist.

**Correct answer:**

Explanation:

Substitute to rewrite this limit in terms of u instead of x. Multiply the top and bottom of the fraction by 2 in order to make this substitution:

(Note that as , .)

, so

, which is therefore the correct answer choice.

### Example Question #4 : Calculus I — Derivatives

Calculate

**Possible Answers:**

The limit does not exist.

**Correct answer:**

Explanation:

You can substitute to write this as:

Note that as ,

, since the fraction becomes indeterminate, we need to take the derivative of both the top and bottom of the fraction.

, which is the correct choice.

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### All High School Math Resources

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