Question

can someone explain how to find the limit for this function:

lim as deltax approaches 0 for 2(x+deltax)- 2x all over deltax

Answer 1

\[
\lim_{\Delta x \rightarrow 0}\dfrac{2(x+\Delta x) - 2x}{\Delta x}
\]

Answer 2

Simplify the numerator.

Answer 3

\[
\lim_{\Delta x \rightarrow 0}\dfrac{2(x+\Delta x) - 2x}{\Delta x} =
\lim_{\Delta x \rightarrow 0}\dfrac{2x+2\Delta x - 2x}{\Delta x} = 2
\]

Answer 4

yes

Answer 5

thank you!!

Answer 6

you are welcome.

Answer 7

but wait i'm still kind of lost wouldnt it be undefined since both delta x equals 0
?

Answer 8

They cancel each other out.

Answer 9

2 * delta x / delta x = 2

Answer 10

Note: When taking limit as delta x approaches zero, remember the delta x does NOT actually become zero. You find the limit as delta x APPROACHES zero. So you are not really dividing zero by zero.

Answer 11

oh okay, i see what you're saying. so the limit would equal to 2. i get it now!

Answer 12

Yes.