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+?

Let flx)= S2x-1 if x>3 what is lim f(x) ? 2x+2ifX<3, what is lim flx)? メ-3 とラメふとす

Given the graph of f(x) at the left, determine the following: a. f(6)= b. lim f(x) = x+2 C. lim f(x) = x-6 d. lim f(x) = x-2- 6- y = f(x) 4- 2- ΟΙ 2 -~ x 2 6 8

Use the graph of f in the figure to find the following values, if they exist. a. f(2) b. lim f(x) X→2 c. lim f(x) X→4 d. lim f(x) X→5 3- 0- 0 13 y = f(x) X