L'Hospital Q: Is it Valid for "Regular" Limits?

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L'Hospital's Rule is specifically designed for limits that yield indeterminate forms like 0/0 or ∞/∞, and its application to "regular" limits is not valid. While applying L'Hospital's Rule to regular limits may yield the same result, it is not appropriate or justified. For example, the limit of (cos(x)+3)/(x+4) as x approaches 0 clearly equals 4/5, while the limit of -sin(x) as x approaches 0 equals 0. Thus, the rule should be reserved for its intended use with indeterminate forms. Misapplying L'Hospital's Rule to regular limits can lead to confusion and incorrect conclusions.
EvLer
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I was just wondering... it is used when the limit is of indetermined form: 0/0 or inf/inf, but is it valid to apply it to a "regular" limit? technically it seems to give the same answer...
 
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If I recall, his rule was to the effect that the ratio of the limits, when the limits are 0 or \infty, is the ratio of the derivatives. That said, you certainly cannot apply it to a regular limit.

As an example, consider the limit:

Lim x->0 (cos(x)+3) /(x+4)

It is clear that the above limit is 4/5.

On the other hand,

Lim x-> 0 (-sin(x))/(1) = 0.

Carl
 
Oh, ok thanks...
 

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