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2 years ago

Which is the range of the function f(x) = 1/7 (9)x

Mathematics

1 answer:

alex41 [277]2 years ago

5 0

It looks incomplete, but all linear functions are going to have *ALL REAL NUMBERS*.

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

5 0

2 years ago

I need help with this one

OlgaM077 [116]

Answer:

112.98 square units

Step-by-step explanation:

Let's work backwards:

Circumference = 2πr

(37.68)/2π = r

Area = π $r^{2}$

Area = π * $((37.68)/2pi)^{2}$

Area = 112.983 square units

3 0

3 years ago

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A rectangle has a perimeter of 71.8 yards and a height of 3.3 yards. What is the length of the base?

Studentka2010 [4]

The length of the base is 32.6

3.3 + 3.3 = 6.6

Subtract 6.6 from 71.8 : 65.2

Divide that by 2 : 32.6

7 0

3 years ago

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Harry, Peter and 7 girls sit in a row. Harry can't sit in an end seat. In how many ways can they be arranged?

Sonja [21]

All possibilities = 9!
possibilities that harry sits at an end = 8! + 8!
possibilities that harry doesn't sit at an end = 9! - 8! -8!

4 0

3 years ago

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What's 25.65 divided by 15

Rasek [7]

25.65 ÷ 15 = 1.71

So, the answer to this problem is 1.17

3 0

3 years ago

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