# How do you find the limit of # sin(7x)/x# as x approaches 0?

##### 2 Answers

7

#### Explanation:

we will use well known limit

so

let

you cannot use LHopital on this <<--- the bit i would like someone else to confirm

#### Explanation:

There are "two" ways to solve this limit. The first way to do is it algebraically, and the second way is to apply L'Hospital's rule (although this is technically incorrect - even though the final answer is the same).

**First way:**

In order to solve this limit, we'd have to use a well-known formula, namely the fact that

Since we have

We can now rewrite our limit in the following way:

If we let

Since we already know what this limit is, we simply substitute:

**Second way:**

To apply L'Hospital's rule, we have to make sure it is an indeterminate form such as

Since direct substitution yields

**Works, but incorrect:**

A more detailed explanation and some more examples on L'Hospital's can be found here.