The lengths of one-year-old baby girls can be described using a normal distribution with a mean of 29 inches and a standard devi
1 answer:
The '68-95-99.7' rule says
-About 68% of values fall within one standard deviation of the mean.
-About 95% of the values fall within two standard deviations from the mean.
-Almost all of the values — about 99.7% — fall within three standard deviations from the mean.
Here
Therefore, the probability
The required probability
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The area of a circle can be found by
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(usually used when finding out the area of a circle)
1.
or 
2.
or 
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or 
4.
The area of a circle can be found by
1.
2.
(Not really sure if this is correct) 3.
4.
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
Since, c = 5 so,
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Find out more information about nth taylor polynomial here
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