For each n = 1,2, 3, ..., define fn (X) = #(1 – a²") for every a e [-1,1] Then the function f defined by f(x) = lim fn (x) exists for each a e [-1,1] and is equal to: S0 if æ| < 1 f(x) = 1 if |r| = 1 {: %3D Sa if|æ| < 1 f(x) = l0 if |r| =1 Ob. O c. f(x) = 0 O d. f(x) = x

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A: The given function is

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A: Show that:

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A:

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A: Graph of function using given information

Q: Sketch a graph of a function f(x) that satisfies all of the following. f(-3) = -3, f(-1) = 2, f(2) =…

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A: lim∆x→07-94+∆x--29∆x The derivative of a function f(x) at the point x = c is, lim∆x→0fc+∆x-fc∆x

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Q: The function f is continuous for all real numbers. If lim f(x) = 0, then what is lim xe-2x)? x-2 x-1

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A: Solution-

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A: Given integral  ∫01x2dx △x=b-an△x=1-0n=1n ci=a+i(△x)ci=0+i1nci= inf(ci)=in2

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A: horizontal compression means horizontal stretch.

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Q: aph each piecewise

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