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seropon [69]
3 years ago
11

Help me please !! The picture is attached

Mathematics
1 answer:
nydimaria [60]3 years ago
6 0

Answer:

  • x+3
  • 5

Step-by-step explanation:

On the interval [-3, -1), the function is a line with a slope of +1 and an x-intercept of -3. It can be described by ...

  f(x) = x +3

__

On the interval [-1, 1] the function is a constant. It can be described by ...

  f(x) = 5

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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.

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3 years ago
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aleksandrvk [35]

Answer:

2

Step-by-step explanation:

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Answer:

For question y=x+3

Your answer is y=(2x+1)+3

Step-by-step explanation:

5 0
2 years ago
4. A triangle has angle measures of 72º and 3°. What is the measure of the third angle?
8090 [49]

Answer:

105

the whole triangle adds up to 180

72+3=75

180-75=105

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Let r= .12 be the reserve rate. What is the money multiplier?
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The money multiplier is 1/ 0.12 
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