## L’Hôpital’s Theorem

L’Hôpital’s Theorem can be used when evaluating limits that have a certain sort of “indeterminate form” (either $$\frac{0}{0}$$ or $$\frac{\pm\infty}{\pm\infty}$$). Subject to some other conditions (What are they? Make sure you check that they’re satisfied!), we can use L’Hôpital’s Theorem to calculate limits like

$\lim_{x\to 0}\frac{\sin x}{x}$

Use L’Hôpital’s Theorem to find the value of this limit for tomorrow’s lesson. Also, what do you think about the result shown below?

$\lim_{x\to 0}\frac{\cos x}{x}=\lim_{x\to 0}\frac{-\sin x}{1}=0$

## The Binomial Theorem

Find the simplified expansion of $$(a+b)^7$$. You can use any method you prefer, but the Binomial Theorem may save you some work!

## Why Study Numbers?

Here’s a link to a recent article about mathematics research. Why do we need to know about prime numbers? Do you know of any important current applications of prime numbers? How would you feel knowing that you were working on solving a problem that may well have no application in your lifetime?

Feel free to share your thoughts below!

## Mock Exams

If you have any questions concerning the mock exam material, you can post them in the comments section below.

Our exams are on Monday Period 4 (paper 1, no calculator) and Tuesday P1 (paper 2).

Good luck!

## Sequences and Series Test

We’ll have our test on Sequences and Series on Tuesday, January 17th.

In order to prepare for the test, complete the following questions.

Pages 200–205 questions 1–3, 5, 6, 9, 13, 19, 23, 25, 27, 29, 35

## Infinite Geometric Series

For tomorrow’s lesson, try to complete page 173 questions 5, 6, 23, 27, and 28.

## Continuous Probability Distributions

Complete the following questions for our lesson tomorrow.

Pages 898–901 questions 1, 2, 7, 11, 19, 20