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# Find values for a constant such that a given limit will exist

Consider the limit expression Find the value of the constant such that this limit will be finite. Find the value of the limit in this case.

We have In order for this limit to exist we must have ; hence . The limit is then 1. tom says:

Oh yeah, I see it now too.

2. tom says:

The answer doesn’t seem right, although it’s the same as the book answer. I’m having a problem seeing how o(1)=1. o(1) means the function will go to zero for any value denominator e>0, doesn’t it? If o(1) did mean 1, then couldn’t we apply any arbitrary constant we want?

• RoRi says:

The answer is right, but I made a mistake in the way I derived (and then an offsetting mistake that got me back to the right answer). As you pointed out . But, in a previous line I dropped a square on the for one of the coefficients. We had in the expansion of , but then when I combined the coefficients for I said it was instead of . When we take them limit we then get the desired . I think it’s all fixed now. Let me know if there’s still a mistake.