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AfilCa [17]
2 years ago
5

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

an = 4n cos(7nπ)
Mathematics
1 answer:
In-s [12.5K]2 years ago
5 0

Answer:

The sequence diverges.

Step-by-step explanation:

A sequence a_{n} converges when \lim_{n \rightarrow \infty} a_{n} is a real number.

In this question, the sequence given is:

a_{n} = 4n\cos{(7n\pi)}

The cosine is always going to be between -1 and 1, so for the convergence of the sequence, we look it as: a_{n} = 4n. So

\lim_{n \rightarrow \infty} a_{n} = \lim_{n \rightarrow \infty} 4n = \infty

Since the limit is not a real number, the sequence diverges.

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Answer:

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Elis [28]

Question 4

<h3>Answer: Choice D</h3>

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

===========================================================

Question 5

<h3>Answer: Choice B</h3>

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

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