# Find the limit for the given function.

• Jan 26th 2008, 05:18 PM
plstevens
Find the limit for the given function.
Find the limit for the given function. http://www.webassign.net/www15/symIm...b5cfe243c9.gif

i know that i need to divide through by x, both top and bottom, but what do i do after this?
• Jan 26th 2008, 05:20 PM
Jhevon
Quote:

Originally Posted by plstevens
Find the limit for the given function. http://www.webassign.net/www15/symIm...b5cfe243c9.gif

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

Quote:

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....
• Jan 26th 2008, 09:58 PM
plstevens
I'm confused i still don't know what to do
• Jan 26th 2008, 10:20 PM
mr fantastic
Quote:

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.
• Jan 27th 2008, 06:32 PM
plstevens
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.
• Jan 27th 2008, 09:06 PM
mr fantastic
Quote:

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.