Six hundred seventy-eight million nine hundred eighty-five thousand four hundred eighty-eight. (I think)
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
6 units to the left of 0 on a number line
So we want to see which number line shows the sum 1.5 + 2.5. We will see that the correct option is <u>"An arrow goes from 0 to 1. 5 and from 1. 5 to 4"</u>
So the number line usually starts at 0 and goes to the first number, 1.5 in this case.
Then, it moves accordingly to the second number, 2.5 (so it will move 2.5 units to the right)
So the number line should start at 0 and move to the right until it meets 1.5 + 2.5 = 4.
From the options, the only that is correct is:
<u><em>"An arrow goes from 0 to 1. 5 and from 1. 5 to 4"</em></u>
If you want to learn more about number lines, you can read:
brainly.com/question/10851163
The inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
<h3>What do you mean by inverse?</h3>
Inverse of the statement means that explain the condition in reverse way or vice versa.
Since, M is the midpoint of PQ, then PM is congruent to QM.
Proving in reverse way, let m be the point between P and Q the distance M from P is equal to the distance from M to Q. Which implies that M lies as the mid of the P and Q.
Thus, the inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
Learn more about inverse here:
brainly.com/question/5338106
#SPJ1