Answer:
The sequence diverges.
Step-by-step explanation:
A sequence
converges when
is a real number.
In this question, the sequence given is:

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

Since the limit is not a real number, the sequence diverges.
Every function is a rule which tells you how to associate inputs and outputs. The input, also known as independent variable, is often indicated with the letter
, while the output, also known as dependent variable, is often indicated with the letter
.
With this notation, we write
, read "y is a function of x", in the sense that the value of the variable y depends on the value of the variable x, and f is the function that tells you how y depends on x.
In your example, you have
, which means "subtract four times the input (4x) from 2"
So, it doesn't matter which input you chose (i.e. the value for x), because you will always have to behave this way:
- Pick an input value, x
- Multiply it by four to get 4x
- Subtract this number from 2: 2-4x
Here are some examples of explicit calculations: if I choose
and input, the workflow will be
- Pick an input value, 2
- Multiply it by four to get 8
- Subtract this number from 2: 2-8=-6
So, if the input is 2, the output is -6
Similarly, if we choose
as input, we have:
- Pick an input value, 0
- Multiply it by four to get 0
- Subtract this number from 2: 2-0=2
So, if the input is 0, the output is 2. And so on: for every possible value for x you have the correspondant value for y, with the function f telling you how to associate one with the other.
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The ten thousands place
hope i helped :)
Answer:
D
Step-by-step explanation:
The radius r is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 5, - 12)
r = 
= 
= 
= 
= 13 → D