What is the difference b/w "Binomial Series" and "Binomial Theorem"? Also give formula for each.
1 answer:
Step-by-step explanation:
The binomial theorem states that for some a,b∈R and some k ∈Z+ ,
(a+b)k=∑n=0k(kn)ak−nbn.
The binomial series allows us to use the binomial theorem for instances when k is not a positive integer. The binomial series applies to a given function f(x)=(1+x)k for any k∈R with the condition that |x|<1 . It is stated as follows:
(1+x)k=∑n=0∞(kn)xn .
Note that the binomial theorem produces a finite sum and the binomial series produces an infinite sum.
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Answer: See Below
<u>Step-by-step explanation:</u>
NOTE: You need the Unit Circle to answer these (attached)
5) cos (t) = 1
Where on the Unit Circle does cos = 1?
Answer: at 0π (0°) and all rotations of 2π (360°)
In radians: t = 0π + 2πn
In degrees: t = 0° + 360n
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Where on the Unit Circle does
<em>Hint: sin is only positive in Quadrants I and II</em>
In degrees: t = 30° + 360n and 150° + 360n
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Where on the Unit Circle does
<em>Hint: sin and cos are only opposite signs in Quadrants II and IV</em>
In degrees: t = 120° + 360n and 300° + 360n
