Solve Limit arctg (x) - Get Help Now

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SUMMARY

The discussion focuses on solving the limit of arctan(x) as x approaches zero, a common problem in Calculus 1. Participants suggest using l'Hôpital's rule and inequalities related to the arctan function, specifically the bounds 0 ≤ arctan(u) ≤ u for u ≥ 0 and -u ≤ arctan(u) ≤ u. The consensus is that understanding the properties of the arctan function is essential for solving the limit effectively.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with l'Hôpital's rule
  • Knowledge of the arctan function and its properties
  • Basic inequality manipulation in calculus
NEXT STEPS
  • Study l'Hôpital's rule in detail and its applications in limit problems
  • Explore the properties and graphs of the arctan function
  • Learn about limit evaluation techniques using inequalities
  • Practice solving limits involving trigonometric functions
USEFUL FOR

Students in Calculus 1, educators teaching limit concepts, and anyone seeking to strengthen their understanding of trigonometric limits and l'Hôpital's rule.

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Homework Statement



I need help solving this limit. If anyone coud«ld help i'd be grateful
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Homework Equations





The Attempt at a Solution



I have no idea how to solve the indetermination...
 
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Did you try l'Hopital's rule?
 
Dick said:
Did you try l'Hopital's rule?

This is a problem for calculus 1, I'm not familiarized with l'Hospital's rule :\
 
Jalo said:
This is a problem for calculus 1, I'm not familiarized with l'Hospital's rule :\

Do you have any inequalities concerning arctan you can use? Something like 0<=arctan(u)<=u for u=>0?
 
Last edited:
Dick said:
Do you have any inequalities concerning arctan you can use? Something like -u<=arctan(u)<=u?

All I've been given was the limit above. I'm supposed to know what's his limit when x tends to zero
 
Jalo said:
All I've been given was the limit above. I'm supposed to know what's his limit when x tends to zero

You have know something about the arctan function to solve it. Can you solve it with the inequality I gave you in the last post? BTW I was sloppy and wrote it incorrectly. I fixed it.
 

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