IMPORTANT!!!

[emiluka2789]

Does anyone have any idea how to solve this...?

Let f(x)=2x+3.  Find lim delta x approaches 0 of    
f(x+ delta x) - f(x)
       delta x

or

lim as x approaches 0 or
sin3x
2x

if you do... iwill love you forever if you can help me in anyway at all!!!

Comments

[thegetupgirl23]

ohmygod it looks like alien writing.
sorry I can't help :\

[emiluka2789]

yeah,.....

[hallock]

This is extremely important to calculus and if you don't fully understand it, I'd suggest talking to your teacher.

f(x) = 2x+3
f'(x) = lim delta x->0

f(x-dx)-f(x)/dx Plug in f(x)
2(x-dx)+3-(2x+3)/dx Simplify
2x-2dx+3-2x+3/dx Remove 2x, add integers
-2dx+6/dx Divide dx out
-2+6 = 4
lim dx x->0 4
= 4

The next one there is a trick that you simply need to memorize:
The trick is lim x->0 sinx/x = 1. Another one you'll want to know is
lim x -> 0 (1-cosx)/x = 0

This problem follows the same premise
lim x->0 sin3x/2x
Since sinx/x = 1 simplify
lim x-> 3/2
= 3/2

[emiluka2789]

thanks a lot! you really helped me with the second one (i had already begged help off of someone else for the first one there)

we didn't actually learn how to do that first bit yet... so i'm not sure why it was in the homework... but yeah. whatever. i'm sure we'll learn it soon?

[nathan_dubetz]

Matt, I don't mean to sound like a dick, but you screwed up the first one. There are some signs that you screwed up. The answer should be two

f(x) = 2x+3
f'(x) = lim delta x->0

f(x+dx)-f(x)/dx Plug in f(x)
2(x+dx)+3-(2x+3)/dx Simplify
2x+2dx+3-2x-3/dx Remove 2x, and integers
2dx/dx Divide dx out
2 = 2
lim dx ->0 2
= 2

[hallock]

I forgot it was minus the quantity itself (2x+3) not -2x+3. Nice catch.

[playcrackmylife]

Is that even a real problem? The only time I've ever seen anything like it was on the ACT, and I think I cried a little then too.

[hallock]

There are far worse.