Problem 4. Let's explore the infinite version of the above result true or not. For each natural number n, we define 1, fn (x) = { if |x| > 1/n n|æ|, if |æ| < 1/n. Explicitly compute g(x) = sup{fi(x), f2(x),-… , fn(x), … }. Is it continuous? ....

Suppose f(n) = 9n² − 16n + 42(log(n))² and g(n) = 4n². Using the formal definition of Big- O, prove that f(n) = O(g(n)) by providing valid constants c, n and proving that they are valid (that the inequality holds). Verify your result by using the limit test described in lecture.

7) State the intervals of concavity in the function h(x) = x2 - 9

2. If you graph the function 1 - el/ x f(x) 1+el/x you will see that f appears to be an odd function. Show algebraically that indeed an odd function f(x) is