3. a) b) For the sequence of functions Find its pointwise limit fn (2) for x = [0, 1]. Justify your answer = Theorem nx² + 2x n x = [0, 1]. f (x) = lim fn(x) n→∞ Show that fnf uniformly on [0, 1]. Justify your answer State the theorem from class which allows to find limn→∞ f¹ fn (x) dx by computing f f (x) dx

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Q: 5) Evaluate the limit of the function f(x) -3x4+4x³+8 lim x→∞0 4x3-5x²+4x-3 -3x4+4x³+8 4x3-5x²+4x-3'…

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Q: x + 3 2x+3 5. (a) Find f(a) for a = -2,-1,0, 1 if f(x) = x + 2 2 4-x for x 1 (b) Find lim f(x) and…

A: Given: For (a), f(-2)=2(-2)+3=-1f(-1)=DNEf(0)=0+2=2f(1)=2

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A: solution:-f(x)=x2-4, for x&lt;0-2,     for x≥0check continuty at x=-2Left hand limitlimx→-2-…

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Q: Prove the following. (b) lim( Vn² +1 – n ") = 0 - (c) lim Vn? n) = } 1 2 ||

A: Prove the following limits

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