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

  • Thread starter Thread starter EvLer
  • Start date Start date
Click For Summary
SUMMARY

L'Hospital's Rule is specifically applicable to limits that present indeterminate forms such as 0/0 or ∞/∞. It is not valid to apply this rule to regular limits, as demonstrated in the example provided: Lim x->0 (cos(x)+3)/(x+4) yields a clear limit of 4/5, while Lim x->0 (-sin(x))/(1) results in 0. The discussion confirms that while L'Hospital's Rule can yield the same numerical result in some cases, its application is strictly limited to indeterminate forms.

PREREQUISITES
  • Understanding of L'Hospital's Rule and its conditions
  • Knowledge of limits in calculus
  • Familiarity with indeterminate forms in mathematical analysis
  • Basic differentiation techniques
NEXT STEPS
  • Study the conditions under which L'Hospital's Rule can be applied
  • Explore examples of limits that are not indeterminate forms
  • Learn about alternative methods for evaluating limits, such as algebraic manipulation
  • Investigate the implications of applying L'Hospital's Rule incorrectly
USEFUL FOR

Students of calculus, mathematics educators, and anyone seeking to deepen their understanding of limit evaluation techniques.

EvLer
Messages
454
Reaction score
0
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...
 
Physics news on Phys.org
If I recall, his rule was to the effect that the ratio of the limits, when the limits are 0 or [itex]\infty[/itex], 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...
 

Similar threads

Slight Confusion in Introductory Mechanics (Dynamics Problem)
  • · Replies 15 ·
Replies
15
Views
1K
How come electric potentials have different signs?
  • · Replies 5 ·
Replies
5
Views
2K
When current flow reach indeterminate form
  • · Replies 3 ·
Replies
3
Views
2K
Electric field lines outside a neutral conducting spherical shell
  • · Replies 12 ·
Replies
12
Views
4K
Is there a limit on how much energy a photon might have in a FOR?
  • · Replies 10 ·
Replies
10
Views
1K
Electric field vector equation: Finding the neutral point for two charges
  • · Replies 35 ·
2
Replies
35
Views
3K
What is the difference in this limit?
  • · Replies 10 ·
Replies
10
Views
2K
Magnetic Field Due to a Curved Wire Segment
  • · Replies 4 ·
Replies
4
Views
1K
Planck's Law: Low, and High Frequency Limit
  • · Replies 3 ·
Replies
3
Views
5K
Find the density of surface charges at the boundary of two conductors with different resistivities
  • · Replies 6 ·
Replies
6
Views
2K