Answer:
A quick hack is often to partially express some function in terms of a Taylor approximation about x0, since higher order terms of x go to zero if we are considering limits for (x−x0)→0. To really answer your question we need to know what the original question was, that is, about which point do you want the expansion? Let us assume around 0. Then we have the Maclaurin series:
cos(x)=1−12x2+O(x4)
You can add more terms if you need to. Now we write:
ln(1+(−12x2))=…
Do you know the standard Maclaurin series for this function?
Hint: it is of the form ln(1+u)
Step-by-step explanation:
1 7/24 is the correct answer I will show you how to get it if needed.
Answer:
I think all of these are optional answers
Step-by-step explanation:
Transformations
(x-3)...: That means the graph shifted 3 units right.
...-1: that means the graph shifted 1 unit down.
answer: 3 units right, and 1 down
Answer:
My sister will swing the total distance = 40 feet
Step-by-step explanation:
On the first swing my sister travels a distance of 8 feet.
In every successive swing she travels 80% of the distance of the previous distance.
So the sequence formed by the distance traveled in every swing will be a geometric sequence.
First term of the sequence 'a' = 8 feet
common ratio 'r' = 0.80
Since this sequence is an infinite geometric sequence,
Sum of this sequence = 
[Since r < 1]
= 
= 
= 40 feet
Therefore, my sister will cover the total distance = 40 feet
