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kherson [118]
3 years ago
14

Given the equations f(x) = x + 4 and d (x) = 2x + 5, find: f (1) + d (2)

Mathematics
1 answer:
Lina20 [59]3 years ago
3 0
1 = x + 4
3 = x

2 = 2x + 5
3 = 2x
3/2= x
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lisabon 2012 [21]
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3 years ago
PLZ HELP!!! Use limits to evaluate the integral.
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Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

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\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

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\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

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<h3><u>Explanation</u></h3>
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<u>\large{(2,-7)}</u>

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