Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
![f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...](https://tex.z-dn.net/?f=f%28x%29%20%3D%20f%28a%29%20%2B%20f%27%28a%29%2A%28x%20-%20a%29%20%2B%20%5Cfrac%7B1%7D%7B2%21%7D%2Af%27%27%28a%29%28x%20-a%29%5E2%20%2B%20...)
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
![f(x) = ln(a) + \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ln%28a%29%20%2B%20%20%5Cfrac%7B1%7D%7Ba%7D%20%2A%28x%20-%20a%29%20-%20%5Cfrac%7B1%7D%7B2%21%7D%20%2A%5Cfrac%7B1%7D%7Ba%5E2%7D%20%2A%28x%20-%20a%29%5E2%20%2B%20%5Cfrac%7B1%7D%7B3%21%7D%20%2A%5Cfrac%7B1%7D%7B2%2Aa%5E3%7D%20%2A%28x%20-%20a%29%5E3%20%2B%20....)
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
Answer: called conditional probability
Answer:
Denote the amount of miles she will run in 24 minutes: x
=> x/24 = 7/60 (same rate)
=> x = 7x24/60 = 2.8 (miles)
Answer:
The first four terms of the sequence are-6, -2, 2 and 6
Step-by-step explanation:
The given sequence is ![a_n=4n-6](https://tex.z-dn.net/?f=a_n%3D4n-6)
In order to find the first four term of the sequence we put n =0, 1, 2 and 3.
For n =0
![a_0=4(0)-6=-6](https://tex.z-dn.net/?f=a_0%3D4%280%29-6%3D-6)
For n =1
![a_1=4(1)-6=-2](https://tex.z-dn.net/?f=a_1%3D4%281%29-6%3D-2)
For n =2
![a_2=4(2)-6=2](https://tex.z-dn.net/?f=a_2%3D4%282%29-6%3D2)
For n =3
![a_3=4(3)-6=6](https://tex.z-dn.net/?f=a_3%3D4%283%29-6%3D6)
Therefore, the first four terms of the sequence are
-6, -2, 2 and 6