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2 years ago

5.2 Q1 - will mark brainliest

Mathematics

1 answer:

sergij07 [2.7K]2 years ago

5 0

In a nutshell, the Riemann's sum that represents the <em>linear</em> equation is A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 5]] - [[4 - (- 6)] / 5], for i ∈ {1, 2, 3, 4, 5}, whose picture is located in the lower left corner of the image.

<h3>How to determine the approximate area of a definite integral by Riemann's sum with right endpoints</h3>

Riemann's sums represent the sum of a <em>finite</em> number of rectangles of <em>same</em> width and with <em>excess</em> area for y > 0 and <em>truncated</em> area for y < 0, both generated with respect to the <em>"horizontal"</em> axis (x-axis). This form of Riemann's sum is described by the following expression:

A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, 3, ..., n}

Where:

a - Lower limit
b - Upper limit
n - Number of rectangle of equal width.
i - Index of the i-th rectangle.

Then, the equation that represents the <em>approximate</em> area of the curve is: (f(x) = 2 · x - 1, a = - 6, b = 4, n = 5)

A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 5]] - [[4 - (- 6)] / 5], for i ∈ {1, 2, 3, 4, 5}

To learn more on Riemann's sums: brainly.com/question/28174119

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valentinak56 [21]

Answer:

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Step-by-step explanation:

We want to find the general limit of the function:

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By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.

So, let's find each one-sided limit: the left-hand side and the right-hand side.

The left-hand limit is given by:

<h3> $\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))$ </h3>

Since the given function is a polynomial, we can use direct substitution. This yields:

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$\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300$

The right-hand limit is given by:

$\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))$

Again, since the function is a polynomial, we can use direct substitution. This yields:

$=(9)^2+2^7+(9.1\times 10)$

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$=300$

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$\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300$

Thus, we can see that:

$\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300$

Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.

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