Answer:
the least integer for n is 2
Step-by-step explanation:
We are given;
f(x) = ln(1+x)
centered at x=0
Pn(0.2)
Error < 0.01
We will use the format;
[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01
So;
f(x) = ln(1+x)
First derivative: f'(x) = 1/(x + 1) < 0! = 1
2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1
3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2
4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6
This follows that;
Max|f^(n+1) (c)| < n!
Thus, error is;
(n!/(n + 1)!) × 0.2^(n + 1) < 0.01
This gives;
(1/(n + 1)) × 0.2^(n + 1) < 0.01
Let's try n = 1
(1/(1 + 1)) × 0.2^(1 + 1) = 0.02
This is greater than 0.01 and so it will not work.
Let's try n = 2
(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267
This is less than 0.01.
So,the least integer for n is 2
Answer:
1a. 1.5
1b. 0.38
Step-by-step explanation:
a.
one full grid is full (1) and half a grid is full (0.5)
b.
there are 100 squares and 38 of them are filled in,so you divide 38 by 100 which is 0.38
Answer:
n - (-4) ≥ 10
4(n+5) ≥ 48
Step-by-step explanation:
n - (-4) ≥ 10
n + 4 ≥ 10
n ≥ 6
4(n+5) ≥ 48
4n + 20 ≥ 48
4n ≥ 28
n ≥ 7
26.74. I’m assuming you are asking what 70% of 38.20 is. 38.20 x 0.70 = 26.74
