The Taylor Series expansion of f(x) = sin(x) about a = π i given by

where the c's are contants.
That is
f(x) = c₀ + c₁(x-π) +c (x-π)² + c₃ (x-π)³ + ...,
₂
The first few derivatives of f(x) are
f' = c₁
f'' = 2c₂ = 2! c₂
f''' = 3.2c₃ = 3! c₃
f⁽⁴⁾ = 4.3.2c₄ = 4! c₄
and so on.
The pattern indicates that

The derivatives of f(x) are
f' = cos(x)
f'' = -sin(x)
f''' = -cos(x)
f⁽⁴⁾ = sin(x(
and so on
The pattern indicates that
f⁽ⁿ⁾(x) = cos(x), n=1,5,9, ...,
= -sin(x), n=2,6,10, ...,
= -cos(x), n=3,7,11, ...,
= sin(x), n=4,8,12, ...,
The radius of convergence is |x-π|<1 by the ratio test.
Answer:
d
plz give me brain liest if im right
Step-by-step explanation:
Answer:
<u>The correct answer s B. 2.21</u>
Step-by-step explanation:
There are three steps to calculate the standard deviation of the set of data given.
n = 5 (5 numbers in the set)
1. Calculate the mean, this way:
(1.2 + 2.3 + 5.2 + 6.6 + 4.8)/5 = 20.1/5 = 4.02
μ = 4.02
2. Calculate the variance, this way:
Sum of the squared difference between each number of the set and the mean divided by the number of elements of the sample minus one.
[(1.2 - 4.02)² + (2.3 - 4.02)² + (5.2 - 4.02)² + (6.6 - 4.02)² + (4.8 - 4.02)²]/4 =
19.568/4 = 4.892
σ² = 4.892
3. Finally, the standard deviation. this way:
Standard deviation is the square root of the variance.
σ² = 4.892
√σ² = √4.892
σ = 2.21
<u>The correct answer s B. 2.21</u>
Answer:
$160
Step-by-step explanation:
Simple interest=principal×time×rate/100
Principal=$800
Time=5years
Rate=4%
S.I=800×5×4/100
S.I=8×4×5
S.I=160
So the simple interest is $160