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4 years ago

Evaluate the following equation: integral from 3 to infinity: 1/(x-2)^(3/2) dx

1 answer:

8 0

The formula in solving the integral of the infinity of 3 is ∫3∞?(1)÷((x−2)(3/2))dx

Substitute the numbers given then solve

limn→inf∫3n(1/((n−2)(3/2))dn

limn→inf[−2/(n−2−−−−−√)−(−2/3−2−−−−√)

=0+2=2

Solve for the integral of 2 when 2 is approximate to 0. Transpose 2 from the other side to make it -2

∫∞3(x−2)−3/2dx=(x−2)−1/2−1/2+C

(x−2)−1/2=1x−2−−−−√

0−(3−2)−1/2−1/2=2

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iren2701 [21]

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2 years ago

Suppose f is a function which follows this pattern, where x and h are any numbers: f(a + h) = f(a)*f(h) Which type of function i

fomenos

$f$ has to be a power function in order to satisfy the recurrence pattern $f(x + h) = f(x) \cdot f(h)$

<h3>Procedure - Determination of a function with a pattern.</h3>

In this case, we must assume a given function and check such assumption fulfill the given recurrence. Let suppose that $f(x) = a^{x}$ , by algebra we have the following property:

$f(x + h) = a^{x+h} = a^{x}\cdot a^{h}$ (1)

And by the definition given in statement, we have the following conclusion:

$f(x+h) = a^{x}\cdot a^{h} = f(x) \cdot f(h)$ (2)

Therefore, $f$ has to be a power function in order to satisfy the recurrence pattern $f(x + h) = f(x) \cdot f(h)$ . $\blacksquare$

To learn more on power functions, we kindly invite to check this verified question: brainly.com/question/5168688

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