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:
If we're measuring in the green the <u>25 degrees</u>
Step-by-step explanation:
80 degrees goes to 90 degrees and then to 100 degrees then to 105 degrees. So 80 to 105.
Answer:
The distance between the tallest building and the statue is 5 miles, so as the statue is inside the range of 7 miles, it can be seen from the tallest building.
Step-by-step explanation:
To solve the problem we need to know the distance between the tallest building in the town and the statue.
This distance can be calculated with the formula of the distance between two points:
d = sqrt(dx^2 + dy^2), where dx is the difference in x-coordinate between the points and dy is the difference in y-coordinate between the points.
So, the distance between these points is:
dx = 5-2 = 3
dy = 1-5 = -4
d = sqrt(3^2 + (-4)^2) = sqrt(9+16) = 5 miles
The distance is 5 miles, so as it is inside the range of 7 miles, the statue can be seen from this point.
Answer:
200:1, Bryn is correct.
Step-by-step explanation:
Each 10 m is represented by a 5cm length on the diagram. We first note that 100 cm = 1 meter. 5 cm is (0.5 cm)*(1 meter/100 cm) =0.05 meters.
The 0.05 meters on the diagram represents 10 meters on the actual building. The ratio is (10 meters/0.05 meters) or 200:1. This is what Bryn believes is the ratio.