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3 years ago

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Mathematics

1 answer:

pantera1 [17]3 years ago

7 0

Answer:

It diverges.

Step-by-step explanation:

We are given the integral: $\int\limits^{-1}_{-\infty} \ln |x| dx$

$\int\limits^{-1}_{-\infty} \ln |x| dx=\int\limits^{-1}_{-\infty} \ln (-x) dx=\\\\= \lim_{t \to \infty} \int\limits^{-1}_{-t} \ln (-x) dx= \lim_{t \to \infty}( x(\ln \left(-x\right)-1))|^{-1}_{-t}=1-\infty=-\infty$

So it is divergent.

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Enter the correct answer in the box. Add the two functions. f(x) = 3x3 + 7x − 26 g(x) = x + 2 Write your answer in the standard

kotykmax [81]

f(x) + g(x) = 3x³ + 8x - 24

that is 3x³ + 7x - 26 + x + 2 = 3x³ + 8x - 24

4 0

3 years ago

Read 2 more answers

I not very good with slope and y intercept form. any tips ?

jeyben [28]

Step-by-step explanation:

To find the slope you use the slope formula which is y2-y2/x2-x1

And to find the y intercept you use y=mx +b. Yous substitute the slope as m and you substitute a point from the line to find b. Which is the y intercept

4 0

2 years ago

Find a particular solution to y" - y + y = 2 sin(3x)

leonid [27]

Answer with explanation:

The given differential equation is

y" -y'+y=2 sin 3x------(1)

Let, y'=z

y"=z'

$\frac{dy}{dx}=z\\\\d y=zdx\\\\y=z x$

Substituting the value of , y, y' and y" in equation (1)

z'-z+zx=2 sin 3 x

z'+z(x-1)=2 sin 3 x-----------(1)

This is a type of linear differential equation.

Integrating factor

$=e^{\int (x-1) dx}\\\\=e^{\frac{x^2}{2}-x}$

Multiplying both sides of equation (1) by integrating factor and integrating we get

$\rightarrow z\times e^{\frac{x^2}{2}-x}=\int 2 sin 3 x \times e^{\frac{x^2}{2}-x} dx=I$

$I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx -\int \frac{2\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx-\frac{2I}{3}\\\\\frac{5I}{3}=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{3}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{3} dx\\\\I=\frac{-2\cos 3x e^{\fra{x^2}{2}-x}}{5}+\int\frac{2x\cos 3x e^{\fra{x^2}{2}-x}}{5} dx$

8 0

2 years ago

Suppose that many large samples are taken from a population and that the

rewona [7]

Answer:

$0.22 -1 *0.029 =0.191$

$0.22 +1 *0.029 =0.249$

And the best option would be:

D. (0.191 to 0.249)

Step-by-step explanation:

For this case we know that the mean is:

$\bar X = 0.22$

And the standard error is given by:

$SE = 0.029$

We want to construct a 68% confidence interval so then the significance level would be :

$\alpha=1-0.68 = 0.32$ and $\alpha/2 =0.16$ . The confidence interval is given by:

$\bar X \pm z_{\alpha/2} SE$

Now we can find the critical value using the normal standard distribution and we got looking for a quantile who accumulate 0.16 of the area on each tail and we got:

$z_{\alpha/2}= 1$

And replacing we got:

$0.22 -1 *0.029 =0.191$

$0.22 +1 *0.029 =0.249$

And the best option would be:

D. (0.191 to 0.249)

5 0

2 years ago

Write the equation of the line in slope-intercept form with slope m=4 through the point (-2,5)

wlad13 [49]

Answer:

y=4x+13

Step-by-step explanation:

Ig, hope it helps

5 0

1 year ago