Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
The total amount of money that was spent by Noel to cash her three (3) most recent paychecks is equal to $10.99.
<h3>What is a paycheck?</h3>
A paycheck can be defined as a financial document that is issued by an employer to an employee as payment for the work done over a period of time.
<h3>How to calculate the amount spent.</h3>
From the table, we can see that the amount of money charged by the bank as check processing fee is equal to $1.99, as well as 1.99% (0.0199) of the amount being cashed by a customer.
Thus, we would compute the amount of money spent by Noel as follows:
Noel = (0.0199 × 100.53) + (0.0199 × 119.38) + (0.0199 × 122.52) + (1.39 × 3)
Noel = 2.00 + 2.38 + 2.44 + 4.17
Noel = $10.99.
Read more on paycheck here: brainly.com/question/26174938
Cost per metre = Rs. 5
Total cost = Rs. 2000
Then total length of the fence = Rs.2000/Rs.5
= 400 metre
Total length of the fence = 400 metre
Answer:
2 and 4
Step-by-step explanation:
This is the only one where the two angles add up to 180 degrees, aka, a straight line.
The answer is E because during 5:00-9:00 the temperature didn’t change
