Limit with trigonometric functions

Click For Summary
The limit of Tanx/(1-Cosx) as x approaches π from the left evaluates to 0, indicating that it does not equal infinity. The second limit, Sec2x/Sinx, also approaches 0 as x approaches π, confirming that both limits are equal and finite. The discussion highlights that L'Hopital's Rule is not applicable since the limits do not present indeterminate forms. The conclusion is that the statement claiming the limits equal infinity is false. Thus, the original assertion is incorrect based on the evaluations provided.
Jules18
Messages
100
Reaction score
0

Homework Statement



True or false?

lim Tanx/(1-Cosx) = lim Sec2x/Sinx = Infinity

(limits are as x approaches \pi from the left)

The Attempt at a Solution



I tried just plugging \pi into x in the first limit, and I ended up getting 0/2, which exists but is just 0. So I said false. Am I simplifying it too much? because what I did seems to make sense but it looks like that's not what they wanted me to do.
 
Last edited:
Physics news on Phys.org


Isn't it just 0/2=0?
 


The original limit was neither of the indeterminate forms [0/0] or [infinity/infinity], so L'Hopital's Rule doesn't apply here. Your first approach was correct.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Use Graph to Determine Limit: Calculating Limits with Piecewise Functions
  • · Replies 3 ·
Replies
3
Views
1K
Finding the limit using a trig identity
  • · Replies 5 ·
Replies
5
Views
2K
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
How Do Limits Behave for Piecewise Functions at Specific Points?
  • · Replies 30 ·
2
Replies
30
Views
2K
Calculation of limit. L'Hopital's rule
  • · Replies 3 ·
Replies
3
Views
2K
Investigating Limit of Piecewise Function
  • · Replies 2 ·
Replies
2
Views
1K
Use the graph of f(x) to investigate the limit
  • · Replies 6 ·
Replies
6
Views
1K
Use Graph To Investigate Limit
  • · Replies 7 ·
Replies
7
Views
1K
Can the limit of a quotient of trig functions approach a specific value?
  • · Replies 2 ·
Replies
2
Views
1K
Limit of 0^0: Evaluating x^sinx
  • · Replies 19 ·
Replies
19
Views
2K