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:
y = -x + 2
Step-by-step explanation:
Lines that are parallel have the same slope but different
y-intercepts.
So the slope of the parallel line is -x
We can input the x and y points given to solve for the new y-intercept
- y = -x + b
- 8 = -(-6) + b
- 8 = 6 + b
- b = 2
The new line is y = -x + 2. Since these two lines are the same, they are coinciding lines.
-Chetan K
Answer:
A) 5 + 2 =7 x 4= 28
B) 8
Step-by-step explanation:
A) 5 x 4 = 20 and 2 x 4 = 8 so you add 20 + 8 and you get 28
B) so 5 x 4 is 20 and there is 8 left over and if you do 2 x 4 you get 8
7 = 2n - 2
n= a number so twice a number is 2n and 7 is 2 less than twice this number.
Answer:
Full proof below
Step-by-step explanation:
