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The fact that there is a tag for problems asking one to find a limit without use of L'Hopital's rule tells me this type of problems is not uncommmon. My question is:

What is the rationale for 'find limit without L'Hopital's rule' problems?

Namely, we develop methods, techniques, and tools so that we are able to solve problems. It does not make sense to me then to (artificially) restrict the tools we have for certain problems.

One reason, in fact, the only one, for the restriction I can think of is pedagogical. If true, then:

Assuming rationale for 'find limit without L'Hopital's rule' is pedagogical, what does one learn while solving a limit without L'Hopital?

I suspect answer to this question comes from the description of the 

limits-without-lhopital
tag. Namely that one learns to "evaluate the limit using standard limit theorems". But then why not to think of problems that do not allow use of L'Hopital's rule since it is not applicable to them.

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    There's at least one good reason *sometimes* for asking without l'Hospital: to force students to develop and sharpen their algebraic, trigonometric, inventive skills. Sometimes even with mathematics students (let alone engineering...), I find out many of them don't really work at ease with fractions, basic trigonometry, factoring and etc. Forcing them to do some limits without l'H is, in these cases and imo, a good idea. – 2017-02-23
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    @DonAntonio I agree, but then why not to come up with problem that does not admit l'H? I understand it might be harder to think of such problems (I make part of my living by teaching as well). – 2017-02-23
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    Coming up with problems that cannot be solved with l'H can be, perhaps, a little hard or way too messy. The issue is to do, sometimes, exercises with stuff that are solvable with l'H witout using it...or something around it, like Taylor series, say. – 2017-02-23
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    Because its so much fun ! – 2017-02-23
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    This has been thoroughly discussed on Meta: http://meta.math.stackexchange.com/questions/13008/why-are-people-so-interested-in-finding-limits-without-lh%C3%B4pitals-rule, http://meta.math.stackexchange.com/questions/18857/using-taylor-expansion-on-a-limit-tagged-without-lhospital – 2017-02-23
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    @HansLundmark Thank you, I went through the limits-without-lhopital tag, but did not think of meta. – 2017-02-23
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    For me the most important reason for such tag here is to convince students that "limits are not the same as plugging" and further that "limits are not the same as differentiating and then plugging". – 2017-02-23

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