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harina [27]
2 years ago
10

Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 eq

ual intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of Integral b a f(x) dx. Which one of the following statements is true?
Lower sum < Trapezoidal rule Value < Upper sum
Lower sum < Upper sum < Trapezoidal rule value
Trapezoidal rule < Lower sum < Upper sum
Cannot be determined without the x-values for the partitions
Mathematics
2 answers:
Umnica [9.8K]2 years ago
5 0

The left sum would be f0+f1+f2+f3

The right sum would be f1+f2+f3+f4

The trapezoidal rule value is:

(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2

This would put the trapezoidal rule in the middle , which makes the answer:

Lower sum < Trapezoidal rule Value < Upper sum

timama [110]2 years ago
5 0

Answer:

Step-by-step explanation:

Given function f(x) is positive, increasing and concave up on the closed interval [a, b],

it means f(x1) < f(x2) if x1 < x2

So Lower sum < Upper sum

As Trapezoidal is average of f(x1) and f(x2) = [f(x1) + f(x2)] / 2

it is average of the Lower and Upper sum.

The answer is Lower sum < Trapezoidal rule Value < Upper sum

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3. Reasoning Ben says that n = 5 is the solution of the equation 7n = 45. How can you check whether Ben is correct? ​
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Step-by-step explanation:

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Which expressions are equivalent to (2^2-9) (x + 3)?
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Answer:

(x^2-3^2)(x+3)

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Step-by-step explanation:

Given

(x^2-9)(x+3)

Required

Select 3 equivalent expressions

(x^2-9)(x+3)

Express 9 as 3^2

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Take x^2 - 3^2 as difference of two squares

(x-3)(x+3)(x+3) -- This is another equivalent expression:

Solving further:

(x-3)(x+3)(x+3) becomes

(x-3)(x+3)^2   -- This is another equivalent expression:

Hence, the equivalent expressions are:

(x^2-3^2)(x+3)

(x-3)(x+3)(x+3)

(x-3)(x+3)^2

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