Working directly from definition, prove that if zn and wn are sequences of complex numbers with limn→∞zn = 4 + 3i, and limn→∞wn = 4 − 3i, then limn→∞zn · wn = 25. (You may use the fact that convergent complex sequences are bounded.)

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A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

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Q: x2, ax + b, -5 sx s-4 x+ 20, x>-4 x<-5 f(x) = The SUM of a and b is -18 25 -19 - 29 18 00000

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Q: 21) Find the fourth degree Taylor poly nomial Centered at C=4 for tue function. 7 (x)=In(x) Anyeuns…

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A: Given: fn(x)=2n2x;            x≤12n2n(1-nx);    12n&lt;x ≤1n0;              1n&lt;x, x∈[0, 1].

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A: According to the definition,  D¯0,1\0=z∈ℂ:0&lt;z≤1 Given sequences are  zn=2eiπ-π2nqn=3ei-π+π2n Now,…

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A: by using techniques of partial fractions and series expansion of 1/(1-x)

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A: Solution:2)b)FalseWe can solve it by taking a simple exampleFourier series of any function f is a0+…

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A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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