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Svetach [21]
3 years ago
14

Find the limit. (If an answer does not exist, enter DNE.) lim Δx→0 (x + Δx)2 − 3(x + Δx) + 2 − (x2 − 3x + 2) Δx

Mathematics
1 answer:
yawa3891 [41]3 years ago
3 0

\displaystyle\lim_{\Delta x\to0}\frac{(x+\Delta x)^2-3(x+\Delta x)+2-(x^2-3x+2)}{\Delta x}

Expand the numerator as

x^2+2x\Delta x+(\Delta x)^2-3x-3\Delta x+2-x^2+3x-2=(2x-3)\Delta x+(\Delta x)^2

Then in the limit,

\displaystyle\lim_{\Delta x\to0}\frac{(2x-3)\Delta x+(\Delta x)^2}{\Delta x}=\lim_{\Delta x\to0}(2x-3+\Delta x)=\boxed{2x-3}

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Answer:

The speed with which Ryan was rowing was 4 mph

Step-by-step explanation:

With a small boat, Ryan wants to row towards an island and come back at a speed of x mph and the island is 20 miles away from him.  

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On the way to the island, there was a wind of 4 mph in the direction of his motion and on the way back also there was a wind of 4 mph in the direction of his motion.

So, in the total journey, he has a speed of (x + 4) mph.

Therefore, \frac{40}{5} = x + 4

⇒ x + 4 = 8

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4 0
3 years ago
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Step-by-step explanation:

6 0
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ZanzabumX [31]

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<em>Iteration 1.</em>

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<em>Iteration 2.</em>

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<em>Iteration 3.</em>

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3 years ago
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