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Svetach [21]
2 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]2 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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daser333 [38]
The given displacement at time, t, is
p(t) = 2 sin(t³) + 5 cos(t³)

The initial equilibrium position is
p(0) = 5

To determine future equilibrium postions, define
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The derivative of f(t) is
f'(t) = (3t²)[2 cos(t³) - 5sin(t³)]

Equilibrium is established when f(t) = 0.
To solve this equation numerically, we shall use the Newton-Raphson method, given by.
t(n+1) = t(n) - f[t(n)]/f'[(t(n)], n=0,1,2, ...,

As a guess, let (0) = 1.
The iterative solution for t is shown below.

  n         t(n)
 ---   -----------
   0   1.0000
   1    0.9344
   2   0.9147
   3   0.9130
   4   0.9130

The solution converges rapidly to t = 0.913 s.
The graphical solution (shown below) confirms the numerical solution.

Answer:
The weight first reaches the equilibrium position in 0.913 sec.

4 0
3 years ago
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The area of the rectangles is 5x2=10 meters squared, while the area of the square is 2x2=4 meters squared.

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Figure A is a scale image of figure B.
Tomtit [17]

Answer:5.25

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11+102 +73 = 186 total killed for ivory = 186 Total killed 19 + 129 + 139 = 287. What percent of the total elephants killed does
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Answer:

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