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7 Μαΐ 2024 · Ex 12.1, 32 If f(x) = { (mx2+n, x<0@nx+m 0≤x≤1@nx3+m, x>1)┤ . For what integers m and n does lim┬(x→0) f(x) and lim┬(x→1) f(x) exist? Given limit exists at x = 0 and x = 1 At x = 0 Limit exists at x = 0 if Left hand limit = Right hand
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It follows that $$\frac{1-x^{n+1}}{1-x}=1+x+x^2+x^3+\cdots+x^n$$ as polynomials, because the equality holds for infinitely many values of $x$ (and we are working over $\mathbb Z$...)
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