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3 years ago

If f(x)=2x+1,then f(-2)=

Mathematics

1 answer:

Sonja [21]3 years ago

8 0

Answer: -3

Explanation: In this problem, we're given the function f(x) = 2x + 1 and we're asked to find f(-2).

To find f(-2) or the value of the function or the value of the function when x = -2, we simply substitute -2 in for x in our function.

So we have f(-2) = 2(-2) + 1 or -4 + 1 which equals -3.

So f(-2) or the value of the function when x = -3 is -3.

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3 years ago

Use the shell method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions

Marina CMI [18]

Answer:

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Step-by-step explanation:

The intersection of the curve $y = x^2$ and $y = 8-x^2$ is

$x^2 = 8 - x^2$

$2x^2 = 8$

$x^2 = 4$

$x = \pm 2$

Since we are rotating the region where $x \geq 0.5$ we will use the intersection x = 2 and y = 4

Using the shell method with x ranges from 0.5 to 2. The volume of the shell would be

$V = \int\limits^2_{0.5} {2\pi x h} \, dx$

where h is the difference between the y-coordinates of the curves, in other words

$h = 8 - x^2 - x^2 = 8 - 2x^2$

Plug h into the V integral and we have

$V = \int\limits^2_{0.5} {2\pi x (8 - 2x^2)} \, dx\\V = 4\pi\int\limits^2_{0.5} {(4x - x^3)} \, dx\\V = 4\pi[2x^2 - x^4/4]^2_{0.5}\\V = 4\pi(2*2^2 - 2^4/4 - 2*0.5^2 + 0.5^4/4)\\V = 4\pi(8 - 4 - 0.5 + 0.015625) \approx 44.18$

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3 years ago