help? sequence?

Question

explain number 3

Answer 1

1).

Yes, as regular polygons increase in the numbers of sides, they look more like circles.

If the number of sides of a regular polygon is large enough, the polygon should be a circle, because,

• In fact, if you have a polygon with very many sides, it looks a lot like a circle from a distance.
• The sides and vertices are evenly spread around a central point, and regular polygons are convex all the vertices point " outwards ".
• In the regular polygon, we can change the number of sides using the controls on the right of the polygon.
• An interesting thing to note is that once the number of sides is quite high (say more than 17) the shape begins to look a lot like a circle.
• In fact, as you keep adding sides, the area of the polygon, the area of its incircle, and the area of its circumference all converge on the same value.

Answer 2

2).

The expression which is read as " The limit of as approaches equals "

 

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behaviour of that function near a particular input.

Informally, a function assigns an output to every input .

The function has a limit at an input if is " close " to whenever is "close" to .

In another words, become closer and closer to as move closer and closer to .

More specifically, when is applied to each input sufficiently close to , the result is an output value that is arbitrarily close to .

If the inputs " close " to are taken to values that are very different, the limit is said to not exist.

Answer 3

3).

Step 1:

First find .

Step 2:

Find .

 

From the above observations :

There is no change about the limit, if the sequence were represented by rather than when approches to .

Solution:

No change about the limit, if the sequence were represented by rather than when approches to .