Given any function f(x), explain why we can evaluate limx→+∞ƒ[g(x)] by substituting t= g(x) and writing 45. (a) Suppose g(x)→+∞ as x→+∞. lim f[g(x)] = lim f(t) - x41x t→+∞ (Here, "equality" is interpreted to mean that either both limits exist and are equal or that both limits fail to exist.) (b) Why does the result in part (a) remain valid if limx→→+ is replaced everywhere by one of limx→∞, limx→c, limx→c-, or limx→c+?

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