Mathematics: Find f. f (x) = 9 + cos x, f(0) = −1, f(7π/2) = 0

Find f. f (x) = 9 + cos x, f(0) = −1, f(7π/2) = 0

Ответ:

nicolacorio02

16.01.2022

Mathematics

For the given function the integrated function is,

$f(x)=\dfrac{9x^2}{2} -cosx+\dfrac{63\pi}{4} x$

Given-

the given equation is,

f"(x)=9+cosx

Integrating both side, we get,

f'(x)=9x+sinx+C_1

Integrating again both side, we get

$f(x)=\dfrac{9x^2}{2} -cosx+C_1x+C_2$

From the given question we have,

f(0)=-1

use this value for the above function, we get,

$f(0)=\dfrac{9(0)^2}{2} -cos0+C_1\times0+C_2$

-1=-1+C_2

C_2=0

from the given question we have,

$f(\dfrac{7\pi }{2} )=0$

With this equation and value of C_2 find the value of the C_1 .

$f(x)=\dfrac{9x^2}{2} -cosx+C_1x+C_2$

$0=\dfrac{9}{2}\times({\dfrac{7\pi }{2}})^2 -cos\dfrac{7\pi }{2}+C_1\dfrac{7\pi }{2}+0$

$0={\dfrac{441\pi^2 }{8}} -0+C_1\dfrac{7\pi }{2}$

$C_1\times\dfrac{7\pi }{2}={\dfrac{441\pi^2 }{8}}$

$C_1=\dfrac{63\pi}{4}$

Put the value of the C_1 and C_2 in the integrated function we get,

$f(x)=\dfrac{9x^2}{2} -cosx+C_1x+C_2$

$f(x)=\dfrac{9x^2}{2} -cosx+\dfrac{63\pi}{4} x+0$

$f(x)=\dfrac{9x^2}{2} -cosx+\dfrac{63\pi}{4} x$

Hence, for the given function the integrated function is,

$f(x)=\dfrac{9x^2}{2} -cosx+\dfrac{63\pi}{4} x$

For more about the integration follow the link below-

link

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Ответ:

josueur9656

16.01.2022

Mathematics

Assuming the conditions are as given and are to be considered boundary values, you have upon integrating twice

$f''(x)=9+\cos x$
$\implies f'(x)=9x+\sin x+C_1$
$\implies f(x)=\dfrac92x^2-\cos x+C_1x+C_2$

When f(0)=-1

, you have

$-1=\dfrac92(0)^2-\cos0+C_1(0)+C_2$
-1=-1+C_2

and when $f\left(\dfrac{7\pi}2\right)=0$ , you get

$0=\dfrac92\left(\dfrac{7\pi}2\right)^2-\cos\dfrac{7\pi}2+C_1\left(\dfrac{7\pi}2\right)+C_2$
$0=\dfrac{441\pi^2}8+\dfrac{7\pi}2C_1$
$C_2=-\dfrac{63\pi}4$

If you meant to include a prime on either of the initial values, then I'll let another user tackle that. The only difference would be the values you find for C_1

and

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Ответ:

Katelyn1236

11.03.2023

Mathematics

interpretation of p-value

With the information from the exercise we can deduce that the number of adults in North America who are going to reduce the costs of medical care, considering this as a national priority, are within a probability of 0.045, however the real data tells us that 0.68 of adults are in favor of this reduction

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Find f.
f ''(x) = 9 + cos x, f(0) = −1, f(7π/2) = 0

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Find f. f ''(x) = 9 + cos x, f(0) = −1, f(7π/2) = 0

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Find f.
f ''(x) = 9 + cos x, f(0) = −1, f(7π/2) = 0