I really need some help with this problem. This is the entire problem :-
Let f(x) = (x^4) + 4 and let Limit of f(x) when x reaches 2 be L.
We will try to make the best possible statement about the upper bounds of |f(x)-L|. What we mean by this can be explained in the following manner.
(1). 3.1 is an upper bound of |2.62|
(2). 2.65 is an upper bound of |2.62|
(3). 2.75 is an upper bound of |2.62|
(4). 2.6 is an upper bound of |2.62|
Now (4) is not even correct. So we should select one from (1), (2) or (3). If we make the statement (2) then we are automatically making the statement (1) and (3). The best one coming the given statements is (2).
Question : Under the condition 0<|x-2|<0.01, find the best statement among the followings:
(a) 0.322618 is an upper bound of |f(x)-L|
(b) 0.322576 is an upper bound of |f(x)-L|
(c) 0.32241 is an upper bound of |f(x)-L|
(d) 0.322392 is an upper bound of |f(x)-L|