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3 years ago

Which function has the range (-∞, 0) and a range of (2, ∞)?

Mathematics

2 answers:

kirill [66]3 years ago

8 0

Answer:

y=sec(x) + 1

Step-by-step explanation:

The Sec(x) = 1/Cos(x) which has a minimum of +1 when positive, and -1 when negative. Adding +1 to it gives a range of (-∞,0) and when negative (2,∞)

Slav-nsk [51]3 years ago

5 0

Wow that is complicated I’m praying for you

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What are the first 4 terms in the sequence represented by the expression 2n+3?

alekssr [168]

Answer:

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

We see that the y-intercept is 10 and the slope is -3

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3 years ago

Definition of piggle

saw5 [17]

Closed shape, do not intersect - geometry definition

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3 years ago

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

$\sum_{n=1}^{inf}\frac{1}{n^p}$

if p>1 then series converges. In oue case we have:

$\sum_{n=1}^{inf}b_n=\frac{1}{n^4}$

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

5 0

3 years ago

An isosceles trapezoid is a quadrilateral with two congruent legs and a pair of parallel bases. Prove the base angles of an isos

Finger [1]

When the sides are congruent (same direction and size), and the two opposite sides are parallel, the angles are the same. In an isosceles triangle, two angles are congruent, because two sides are congruent.

3 0

3 years ago

Read 2 more answers