How to Evaluate Limits with ln(pi) and ln(4)?

  • Thread starter fishingspree2
  • Start date
  • Tags
    Limit
In summary, the conversation is about evaluating a limit and using the l'Hospital rule to solve for the infinite/infinite problem. The conversation also discusses rewriting a fraction using Euler's number as a base and using ln(pi) and ln(4) to solve for eax - bx = e(a-b)x.
  • #1
fishingspree2
139
0
Hello,

How would someone evaluate this limit?? :confused:
http://img407.imageshack.us/img407/9899/14403274.gif

I can't get rid of the infinite/infinite problem using l'hospital rule :confused:

thank you
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Rewrite the fraction using the same base for each power so that you can express it as Af(x). Ie., Euler's number e makes a useful base.
 
  • #3
you mean like that? http://img242.imageshack.us/img242/8780/58121121.gif
or like that ? http://img172.imageshack.us/img172/9394/47770366.gif
sorry I don't really know how :confused:
 
Last edited by a moderator:
  • #4
Pi is ea for some number a while 4 is eb for some number b. In particular, those numbers are ln(pi) and ln(4). We then have eax - bx = e(a-b)x.
 

FAQ: How to Evaluate Limits with ln(pi) and ln(4)?

What is a limit?

A limit is a fundamental concept in calculus that represents the value that a function approaches as the input approaches a certain point.

How do you evaluate a limit?

To evaluate a limit, you can use various methods such as direct substitution, factoring, and algebraic manipulation. You can also use graphing or numerical methods to approximate the limit value.

What are the steps to evaluate a limit?

The steps to evaluate a limit include:

  1. Identify the value that the input is approaching.
  2. Simplify the function using algebraic manipulation, if possible.
  3. Substitute the value of the input into the simplified function.
  4. If the resulting expression is undefined, try using other methods to evaluate the limit.
  5. If the resulting expression is defined, then that is the limit value.

What are some tips for evaluating limits?

Some tips for evaluating limits include:

  • Simplify the function before substituting the input value.
  • Check for any common factors that can be cancelled out.
  • For trigonometric functions, use trigonometric identities to simplify the expression.
  • For rational functions, check if the function is undefined at the input value and apply the rules of limits accordingly.
  • If you are unsure of how to evaluate a limit, try using a graphing calculator or a table of values to approximate the limit value.

Why is it important to evaluate limits?

Evaluating limits is important because it helps us understand the behavior of a function at a specific point. It also allows us to solve complex problems in calculus, such as finding the slope of a curve or determining the area under a curve.

Similar threads

I To What Extent Can You Manipulate Limits?
Replies
9
Views
494
MHB 3.4.238 AP calculus exam Limits with ln
Replies
1
Views
1K
MHB Evaluate Limit: $\frac{0}{0}$ - Can Someone Help?
Replies
4
Views
1K
MHB Evaluating Limit Using L'Hospitals Rule $\tiny{205.q4.1}$
Replies
3
Views
2K
MHB Find the limit as x goes to infinity
Replies
5
Views
2K
MHB Derivative and Limit of an Exponential Function
Replies
3
Views
2K
MHB Limits with the natural logarithm
Replies
3
Views
1K
MHB Calculating Limits without Cheating or L'Hopital's Rule
Replies
5
Views
2K
B Question about the limits of integration in a change of variables
Replies
2
Views
1K
MHB How Can You Solve This Limit Problem Without L'Hospital's Rule?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top