# Thread: Find the limit for the given function.

1. ## Find the limit for the given function.

Find the limit for the given function.

i know that i need to divide through by x, both top and bottom, but what do i do after this?

2. Originally Posted by plstevens
Find the limit for the given function.
note that: $\displaystyle \frac {\sin 4x}x = \frac 44 \cdot \frac {\sin 4x}x = 4 \cdot \frac {\sin 4x}{4x}$

thus: $\displaystyle \lim_{x \to 0} \frac {\sin 4x}x = 4 \lim_{x \to 0} \frac {\sin 4x}{4x}$

now continue

Hint: this is in the form of a special limit

i know that i need to divide through by x, both top and bottom, but what do i do after this?
that would make no sense, you'd end up with exactly the same thing....

3. I'm confused i still don't know what to do

4. Originally Posted by plstevens
I'm confused i still don't know what to do
Do you know that $\displaystyle \lim_{z \rightarrow 0}\frac{\sin z}{z} = 1$?

What Jhevon has done is re-write your limit into this form (so z = 4x in this particular case).

So the answer is (4)(1) = 4.

5. ## which are continuous functions

Which of the following are continuous functions? (Select all that apply.)

The temperature at a specific location as a function of time.
The temperature at a specific time as a function of the distance due west from New York City.
The altitude above sea level as a function of the distance due west from New York City.
The cost of a taxi ride as a function of the distance traveled.
The current in the circuit for the lights in a room as a function of time.
None of these.

6. Originally Posted by plstevens
Which of the following are continuous functions? (Select all that apply.)

The temperature at a specific location as a function of time.
The temperature at a specific time as a function of the distance due west from New York City.
The altitude above sea level as a function of the distance due west from New York City.
The cost of a taxi ride as a function of the distance traveled.
The current in the circuit for the lights in a room as a function of time.
None of these.
Memo: Start a new thread for a new and unrelated problem. This question has been answered here.