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The rate of​ healing, A′(t)​(in square centimeters per​ day), for a certain type of abrasive skin wound is given approximately by the table.

t 0 1 2 3
A′(t) 0.91 0.83 0.76 0.69

t 4 5 6 7
A′(t) 0.62 0.58 0.48 0.44 ​

Use left and right sums over five equal subintervals to approximate the area under the graph of A′(t) from t=0 to t=5.

The left​ sum, L5​, is __________.
The right​ sum, R5​, is ______________.

Respuesta :

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Answer:

Step-by-step explanation:

Given that:

t          0           1              2          3            4            5           6            7

A'(t)    0.91       0.83       0.76     0.69       0.62      0.58      0.48      0.44

a)  [tex]\Delta x = \dfrac{5-0}{5}[/tex]

[tex]\Delta x = 1[/tex]

[tex]L_ 5= \Delta x ( (A'(0)+A'(1)+A'(2)+A'(3)+A'(4)) \\ \\ = 1 (0.91 + 0.83+ 0.76 +0.69 + 0.62 ) \\\\ L_5 =1( 3.81) \\ \\ \mathbf{L_5 = 3.81}[/tex]

[tex]R_ 5= \Delta x ( (A'(1)+A'(2)+A'(3)+A'(4)+A'(5)) \\ \\ = 1 ( 0.83+ 0.76 +0.69 + 0.62 +0.58) \\\\ R_5 =1( 3.48) \\ \\ \mathbf{R_5 = 3.48}[/tex]

The true statement:

[tex]Since, R_5 = 3.48 \ and \ L_5 = 3.81; \\ \\ Then : R_5 \le \int \limits ^5_0 A'(t) dt \le L_5[/tex]

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