Question

how do you find the limit of an equation with a delta symbole like this.............???????????????

Answer 1

epsilon-delta

Answer 2

missing the question
something like
\[\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}\] ?

Answer 3

hold on my computerws slow i putting it up now

Answer 4

Do you mean formally proving a limit using delta-epsilon notation?

Answer 5

\[\lim_{Deltax \rightarrow 0} 2(x+Deltax-2x)/Deltax\]

Answer 6

use the definition of a limit

Answer 7

\[\lim_{h\to 0}\frac{2(x+h)-2x}{h}\] is easier to write

Answer 8

do the algebra first, get
\[\frac{2(x+h)-2x}{h}=\frac{2x+2h-2x}{h}=\frac{2h}{h}=2\]

Answer 9

you will recognize this as the slope of the line \(y=2x\) since you are computing the change in \(y\) over the change in \(x\)
since this is a line, the slope is constant, and it is 2

Answer 10

notice that when you get done the algebra, you get a constant, that does not depend on \(x\)
that is because this is a line
slope doesn't change

Answer 11

yess its and intro to calc AP

Answer 12

Think about what satellite said, and how you could apply to finding the slope of non-linear functions (like a parabola).

Answer 13

ok then, would this one work the same way ??....\[\lim_{h \rightarrow 0} (x+h)^{2}-2x/h\]

Answer 14

\[x ^{2}+h ^{2}-x ^{2}/h\]

Answer 15

I think you mean
\[\lim_{h\rightarrow 0} \frac{(x+h)^2 - x^2}{h}\]

Answer 16

yes

Answer 17

What does that evaluate to?

Answer 18

use FOIL to do (x+h)(x+h)

Answer 19

ok were do i go from here

Answer 20

\[\lim_{h\rightarrow 0}\frac{(x+h)^2-x^2}{h}\\
\lim_{h\rightarrow 0}\frac{x^2+2xh+h^2-x^2}{h}
\]
Can you find the limit?

Answer 21

do i know sub in 0 for h

Answer 22

now not know

Answer 23

always simplify first

Answer 24

how much further can i simplify

Answer 25

x^2-x^2 looks promising

Answer 26

do i cross out the h's

Answer 27

Yes, you can do that after removing the x^2's. Can you then plug in h=0 without dividing by 0?

Answer 28

yes

Answer 29

arent u left with 2x

Answer 30

or did i do something wrong?

Answer 31

Sorry for the late response (computer issues). Yes, that's correct. You get 2x. So if that limit gives you the slope, what does 2x mean?

Answer 32

2/1 ? idk @mboorstin

Answer 33

I'm talking about the fact that a parabola's slope is 2x. What that means is that you can find the slope of a non-linear function, but that the slope is variable depending on the location of the function. Not a big deal if you don't get it right now, you'll spend a few days in class talking about it. Your limits were correct, but that's why (f(x+h)-f(x))/h is so important.

Answer 34

oh ok thanks you for the exlaination