Question

need help with problem

Answer 1

For the BADLIM, we can pick this function as an example:

\[f(x)=\frac{1}{x}\]

So, for every M > 0 we choose, there exists a value x > 0
(and in our case we will pick this one:)

\[x=\frac{1}{M+1}\]

so, plugging this x-value into the function:

\[f(\frac{1}{M+1})=M+1 > M\]

The conditions of BADLIM are satisfied.
However, what's "wrong" here, is that as the values of M we choose increase,
the range of values of the corresponding x's we can choose decreases and we gets closer and closer to 0, instead of growing away from 0 towards infinity.



also, we know that

\[\lim_{x \rightarrow \infty} \frac{1}{x} = 0\]

And the below is wrong (even though it satisfies the definition of BADLIM):

\[\lim_{x \rightarrow \infty} \frac{1}{x} = \infty\]

Answer 2

Thanks!