1. If g(x)= 3 + x + e^x, find g^-1(4).
It seems as if I cannot isolate "x" by itself.
2. lim x / ( √(1+3x) - 1 )
I know the answer is 2/3 (due to graphing), but I cannot prove this answer utilizing the Limit Laws.
3. A Tibetan monk leaves the monastery at 7:00 A.M. and takes his usual path to the top of the mountain, arriving at 7:00 P.M. The following morning, he starts at 7:00 A.M. at the top and takes the same path back, arriving at the monastery at 7:00 P.M. Use the Intermediate Value Theorem to show that there is a point on the path that the monk will cross at exactly the same time of day on both days.
I am utterly stumped on this problem. I realize that I have to chart the path on the same graph, but then what?
4. Find lim x⇒->∞ f(x) if, for all x > 1,
5√(x) / (√(x-1)) < f(x) < (10e^x - 21) / (2e^x)