# Binomial expansion to find limitsWatch

Thread starter 1 week ago
#1
https://mathsorchard.weebly.com/uplo...1819/1998.docx

Concerning 1998 STEP 3 question 3...

In the given solution the expression found for Vn has c as a denominator, and I'm wondering why that doesn't pose any problems for evaluating at c=0. Is it simply because everything in the bracket disappears before the denominator by rules of precedence?

Also, is the binomial expansion absolutely necessary there? Because without it it's unclear whether the final term tends to zero or infinity?

Is there no other way to deduce that the limit as c tends to zero is the same as the value when c = 0 ? Is this fact less obvious than it sounds to me to be?

Thanks.
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1 week ago
#2
(Original post by jameshyland29)
https://mathsorchard.weebly.com/uplo...1819/1998.docx

Concerning 1998 STEP 3 question 3...

In the given solution the expression found for Vn has c as a denominator, and I'm wondering why that doesn't pose any problems for evaluating at c=0. Is it simply because everything in the bracket disappears before the denominator by rules of precedence?
There *is* an issue with evaluating at , which is why the limits are used to justify the statement .

Also, is the binomial expansion absolutely necessary there? Because without it it's unclear whether the final term tends to zero or infinity?

Is there no other way to deduce that the limit as c tends to zero is the same as the value when c = 0 ? Is this fact less obvious than it sounds to me to be?

Thanks.
You don't *need* to use the binomial expansion here, but it does make it a whole lot clearer as to what the limit must be because you are then able to cancel out the in the denominator.

An alternative approach is to use L'Hopitals rule:

.

In addition to that, since that means .
Last edited by RDKGames; 1 week ago
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