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Maurinko [17]
3 years ago
15

Given:An = [6 n/(-4 n + 9)]For both of the following answer blanks, decide whether the given sequence or series is convergent or

divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.(a) The sequence {An }._________________(b) The series ∑n=1∞( An )_____________________Note: In order to get credit for this problem all answers must be correct.please show all steps. I must be makeing asilly mistake. thanks
Mathematics
1 answer:
Mrrafil [7]3 years ago
7 0

Answer:

The sequence is convergent and the serie is divergent.

Step-by-step explanation:

Sequence:

We calculate the limit when n tends to infinity to see if it is convergent or divergent:

\lim_{n \to \infty} \frac{6n}{-4n+9} = \frac{6}{-4} = \frac{-3}{2} \neq 0 then, the sequence is convergent.

Serie:

\sum_{n=1}^{\infty} (\frac{6n}{-4n+9}). To know if it converges we are going to use the limit test:

\lim_{n \to \infty} a_n. If this limit is non equal to 0 the serie diverges.

\lim_{n \to \infty} \frac{6n}{-4n+9} = \frac{6}{-4} = \frac{-3}{2} \neq 0, then the serie diverges.

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PLEASEEE HELPPPP IM BEGGIN U
Anna71 [15]

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

  • the variables are omitted ("place value" is used instead)
  • the constant in the divisor is <em>negated</em> so its product with the partial quotient can be <em>added</em> to obtain the new dividend
  • the divisor binomial is assumed to have a leading coefficient of 1.

__

<h3>a) </h3>

The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

<h3>b)</h3>

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

__

<h3>c)</h3>

The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  \begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}

__

<h3>d)</h3>

The second attachment shows synthetic division by the factor (x+4).

_____

<em>Additional comment</em>

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

6 0
2 years ago
Need help!!!! Pleaseeeee
Amanda [17]

Answer:

for #2 I'm pretty sure he makes $10 per hour

6 0
2 years ago
How do you simplify rational expressions
tatiyna

1) Look for factors that are common to the numerator & denominator

2) Cancel the common factor

3) If possible, look for other factors that are common to the numerator and denominator.

Hope this helps☺

Correct me if im wrong



3 0
3 years ago
II. Let f(x) = 9 – x , g(x) = x2<br> + 4, and h(x) = x – 2. Compute the following:<br> 7. g(f(12))
Alex17521 [72]
G(f(12))
f(12) = 9 - 12 = -3
g(-3) = (-3)^2 + 4 = 9 + 4 = 13
4 0
2 years ago
Is x = 1 a solution of the equation 2 – 8x = –6?
borishaifa [10]

Let's verify by substituting 1 to x.

2 - 8x = -6

2 - 8(1) = -6

2 - 8 = -6

-6 = -6

It is equal, therefore x = 1 is the solution.

4 0
3 years ago
Read 2 more answers
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