Is the statement "if the limit of f(x) as x approaches c is 0, then there must exist a number k such that f(k)<0.001" a true or false statement?

Question

Is the statement "if the limit of f(x) as x approaches c is 0, then there must exist a number k such that f(k)<0.001" a true or false statement?

1 Answer

Impact of this question

7388 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-04T00:49:48

It is true.

Explanation:

If #lim_(xrarrc)f(x) = 0#, the for any positive #epsilon#, (like #0.001#) there is a positive #delta# such that for every #x# with #0 < abs(x-c) < delta# we have #abs(f(x)-0) < epsilon#.

There is not only one value of #k#, but for the #delta# that works for #epsilon = 0.001#, every #x# in #(c-delta, c+delta)# has #absx < 0.001#, so it has #f(x) < 0.001#

Science

Math

Humanities

... and beyond

Is the statement "if the limit of f(x) as x approaches c is 0, then there must exist a number k such that f(k)<0.001" a true or false statement?

1 Answer

Explanation:

Related questions

Impact of this question