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Ira Lisetskai [31]
3 years ago
7

At the beginning of summer, the water level on a pond is 2 feet below its normal level. After an unusually dry summer, the water

level on the pond dropped another 2 feet. How far above or below the normal water level is the pond at the end of the summer?
Mathematics
1 answer:
Scilla [17]3 years ago
8 0

Answer:

Step-by-step explanation:

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A. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic appr
Tema [17]

Answer:

a. p1(x) = 2 - x

b. p2(x) = x² - 3*x + 3

c. p1(0.97) = 1.03; p2(0.97) = 1.0309

Step-by-step explanation:

f(x) = 1/x

f'(x) =  -1/x²

f''(x) = 2/x³

a = 1

a. The linear approximating polynomial is:

p1(x) = f(a) + f'(a)*(x - a)

p1(x) = 1/1 + -1/1² * (x - 1)

p1(x) = 1 - x + 1

p1(x) = 2 - x

b. The quadratic approximating polynomial is:

p2(x) = p1(x) + 1/2 * f''(a)*(x - a)²

p2(x) = 2 - x + 1/2 * 2/1³ * (x - 1)²

p2(x) = 2 - x + (x - 1)²

p2(x) = 2 - x + x² - 2*x + 1

p2(x) = x² - 3*x + 3

c. approximate 1/0.97 using p1(x)

p1(0.97) = 2 - 0.97 = 1.03

approximate 1/0.97 using p2(x)

p2(0.97) = 0.97² - 3*0.97 + 3 = 1.0309

7 0
3 years ago
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