Find the limit (if it exists). (If an answer does not exist, enter DNE.) $ \displaystyle{\lim_{\Delta x \rightarrow 0}} \text{ } \dfrac{{\color{red}2} (x + \Delta x) - {\color{red}2} x}{\Delta x} $

2x - 2

Step-by-step explanation:

Here is the completer question

lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx

Solution

lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx

Expanding the brackets, we have

lim as Δx → 0 [(x² + 2xΔx + (Δx)²- 2x - 2Δx + 3 - x² + 2x - 3)]/Δx

Collecting like terms. we have

lim as Δx → 0 [(x² - x² + 2xΔx - 2Δx + (Δx)²- 2x  + 2x + 3 - 3)]/Δx

Simplifying, we have

lim as Δx → 0 [(0 + 2xΔx - 2Δx + (Δx)² + 0 + 0)]/Δx

lim as Δx → 0 [2xΔx - 2Δx + (Δx)²]/Δx

Dividing through by Δx, we have

lim as Δx → 0 [2x - 2 + (Δx)]

Inserting Δx = 0, we have

= lim as Δx → 0 (2x -2 + 0)

= 2x -2

So lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx = 2x -2

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)