99 POINT QUESTION PLUS BRAINLIEST!!!

1 answer:

6 0

Yay, I like das stuff

I think I learned the washer method
goes like this

$area=\pi \int\limits^a_b {(outercurve)^2-(innercurve)^2} \, dx$

ok, so

actuallly, this is easier

y=49-x^2 and
y=0
see when they intersect again
they intersect at -7 and 7
if we do integrate from -7 to 7, then it wil give 0 (because integration is area under the curve), so note that they are same both sides so integrate from 0 to 7 then double the volume to get both sides
so it can't be C or D
It also can'nt be A because it should not be multipied by 4, it should be multipied by 2

basically, we don't need the washer method
remember, area=pir^2
the disk method then
we are summing up all the radii disks and squareing them
but doubleing them so
$area=2\pi (\int\limits^7_0 {49-x^2} \, dx )^2$
no idea why we need the inside part to be x(49-x^2), that is intersting

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Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$