Answer: Arithmetic Sequence
Step-by-step explanation:
An Arithmetic Sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.
Answer:
The bottle of orange juice will have higher amounts of vitamin C per serving, as it will have 125 mg against 90 mg of the cranberry juice.
Step-by-step explanation:
To determine the amount of vitamin C in each serving of fruit juice, knowing that the bottle of orange juice contains 750 mg of vitamin C and 6 servings, while the bottle of cranberry juice contains 135 mg and 1.5 servings, you must perform the following calculation:
Orange: 750/6
Orange: 125 mg per serving
Cranberry: 135 / 1.5
Cranberry: 90 mg per serving
Thus, the bottle of orange juice will have higher amounts of vitamin C per serving, as it will have 125 mg against 90 mg of the cranberry juice.
Answer:
1638
Step-by-step explanation:
3(500)+3(40)+3(6)=1500+120+18=1638
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
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