Question

Is this problem do-able? Proving limits of f(x) = 0 and g(x) is bounded ....

Answer 1

Prove that if \[\lim_{x \rightarrow a}f(x)=0 \] and g(x) is bounded, then \[\lim_{x \rightarrow a}f(x)g(x)=0\]

Answer 2

topic of "bounded" from precalculus book:

Upper and Lower Bound Rules:
Let f(x) be a polynomial with real coefficients and a positive leading coefficient. Suppose f(x) is divided by x-c, using synthetic division.

1. If c > 0 and each number in the last row is either positive or zero, c is an "upper bound" for the real zeros of f.

2. If c < 0 and the numbers in the last row are alternately positive and negative (zero entries count as positive or negative), c is a "lower bound" for the real zeros of f.

Answer 3

No one in my calculus class was able to solve this, we just finished chapter 2 covering limits. One male student asked where he could get the information to solve this problem, since CH 1 (Algebra & Trig. Review) and CH 2 (Limits) does not talk about this type of problem.

Professor mentioned, that the author of the textbook "assumed that students know how to do this" and that our previous professors for precalculus and algebra 2 should of covered the topic of "bounded." I scanned through the precalculus book, and only found one small section that mentions "bound" and algebra 2 book doesn't even talk about it.

A tutorer at my college, who is taking linear algebra never seen this type of problem also. So, I don't know if our professor is screwing with us or not. lol. This problem is created by the professor.