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dsp73
3 years ago
14

Match the estimated value of each expression with its position on the number line ​

Mathematics
2 answers:
allochka39001 [22]3 years ago
5 0

Answer:going down d,c,e,a

Step-by-step explanation:

Natalka [10]3 years ago
4 0

Answer:

I did the same thing i just finished so the answer is dcea.

Step-by-step explanation:

All you have to do when working the fractions is solve the top then solve the bottom then when you get the fraction reduced after solving the top and bottom just simplify what is left over.

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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0
3 years ago
Sus crib ete a mi canal de You tube me llamo <br><br>Leeom 47<br><br>porfa​
Alex Ar [27]

Answer:

Ightt

Step-by-step explanation:

7 0
2 years ago
What is 3x=5x+9<br> btw im just giving out points but u can still answer
Leviafan [203]
The correct answer is -9/2
5 0
2 years ago
Read 2 more answers
A horse travels 100 meters at a velocity of 30m/s W. How long does it take the horse to travel this distance?
Dafna1 [17]

The formula for finding time is the distance divided by the velocity.So the answer is 100÷30=3.3333...

6 0
3 years ago
Any one good at factoring?
svetlana [45]
The student went wrong in step three.  the solutions should have been -3 and 5
8 0
3 years ago
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