1. ## Quick Limit Question

If there is a limit, for example:

lim (x-->0) [(5-k)/x]

where k is a constant and i needed to find values (if any) of k such that the limit exists.

Would k=5 be the only value for k that would make the limit exist, and in this case the limit is equal to 0? Or does the limit still not exist?

Thanks

2. Originally Posted by trivial123
If there is a limit, for example:

lim (x-->0) [(5-k)/x]

where k is a constant and i needed to find values (if any) of k such that the limit exists.

Would k=5 be the only value for k that would make the limit exist, and in this case the limit is equal to 0? Or does the limit still not exist?

Thanks
If k = 5 then the expression you're taking the limit of is the same 0. And it is trivial but true that $\displaystyle \lim_{x \rightarrow 0} 0 = 0$.

3. Thanks for the reply, thought so. But is k=5 the only value of k for which the limit exists?

4. Originally Posted by trivial123
Thanks for the reply, thought so. But is k=5 the only value of k for which the limit exists?
If k is a constant, the numerator is going to be a constant for any value of k. The rational function $\displaystyle y=\frac{a}{x}$, where a is a constant, doesn't have a valid limit at 0.