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3 years ago

Given the graph of the function f(x) below what happens to f(x) when x is a very small positive number?

Mathematics

1 answer:

vladimir2022 [97]3 years ago

4 0

Answer: The correct option is

(B) f(x) is a very large positive number.

Step-by-step explanation: We are given the graph of a function f(x) as shown in the figure.

We are to check what happens to the f(x) when x is a small positive integer.

From the graph, we see that

when x is approaching to 0 from left hand side, then the value of f(x) is approaching to negative infinity.

And,

when x is approaching to 0 from right hand side, then the value of f(x) is approaching to positive infinity.

So, when x is a very smell positive integer, then y is approaching to positive infinity.

That is, the value of f(x) is a very large positive number.

Option (B) is CORRECT.

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13p + 5p - 9p -2p=7 what is p

Law Incorporation [45]

Answer:

p=1

Step-by-step explanation:

18p-9p=9p

9p-2p=7p

7p=7

6 0

3 years ago

HELP ME PLEASE!!! The function f(x) is graphed on the coordinate plane. What is f(−2) ? Enter your answer in the box. f(−2) =

Ksenya-84 [330]

Answer:

f(-2)=-2

Step-by-step explanation:

we know that

x -----> is the independent variable or input value

f(x) ---> is the dependent variable or output value

f(-2) is the value of the function f(x) when the value of x is equal to -2

For x=-2

Looking at the graph

f(-2)=-2

For an input value of -2 the output value is -2

5 0

3 years ago

Please help me out and help me show work ??

DochEvi [55]

Answer:

23 is the smallest number

Step-by-step explanation:

Three consecutive numbers are numbers that come in a row. So if the first number is n then the next is n+1 and the following is n+2.

All together they add to 72.

So n + n+1 +n +2 = 72.

3n + 3 = 72

3n = 69

n = 23

8 0

3 years ago

to build the garden of your dreams you need 11 m^3 of coil containing 46% clay. you have two types of soil you can combine to ac

aivan3 [116]

Answer: 9m^3 of soil with 50% clay and 2m^3 of soil with 28% clay is required

Step-by-step explanation:

Let x represent the quantity of the soil containing 50% clay that you would use.

Let y represent the quantity of the soil containing 28% clay that you would use.

To build the garden of your dreams you need 11 m^3 of soil.

x + y = 11 - - - - - - - - -1

Since the soil must contain 46% clay, the total amount of clay required is 46/100 × 11 = 5.06 m^3.

you have two types of soil you can combine to achieve this: soil with 50% clay and soil with 28% clay. This means that the quantity of both soils required to achieve 5.06 m^3 will be

0.5x + 0.28y = 5.06 - - - - - - - -2

Substituting x = 11 - y into equation 1, it becomes

0.5(11 - y) + 0.28y = 5.06

5.5 - 0.5y + 0.28y = 5.06

- 0.5y + 0.28y = 5.06 - 5.5

- 0.22y = - 0.44

y = - 0.44/ -0.22 = 2

Substituting y = 2 into x = 11 - y, it becomes

x = 11 - 2 = 9

7 0

4 years ago

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y

DiKsa [7]

The area of the surface is given exactly by the integral,

$\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx$

We have

$y(x)=\dfrac15x^5\implies y'(x)=x^4$

so the area is

$\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx$

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the $i$ -th subinterval are, respectively,

$\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2$

$r_i=\dfrac{5-0}{10}i=\dfrac i2$

with midpoint

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

with $1\le i\le10$ .

Over each subinterval, we interpolate $f(x)=\sqrt{1+x^8}$ with the quadratic polynomial,

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

Then

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that the latter integral reduces significantly to

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)$

which is about 651.918, so that the area is approximately $651.918\pi\approx\boxed{2048}$ .

Compare this to actual value of the integral, which is closer to 1967.

4 0

3 years ago