Limit Problem: 1/b - 1/3 as b approaches 3 | Homework Help

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In summary, the conversation discusses finding the limit of an expression involving fractions and simplifying the expression to find the answer. The individual tried various methods such as direct substitution, using a conjugate, and simplifying the expression, but was unable to find the answer until realizing that they needed to take the difference of the two fractions. The final answer was -1/9.
  • #1
EvilBunny
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Homework Statement


1/b - 1/3
-----------
b-3



Lim b ----> 3


Homework Equations





The Attempt at a Solution




This is driving me nuts. I always end with 0 but that's not the answer.
I tried direct substitution and it didn't work.

I tried plugging in 2.999999999 but it gives a very small number devided by a very small number

I tried the conjugate and even deviding by the highest power altho that's for infinity.
 
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  • #2
You can try this experimentally to see what the limit (if any) appears to be. It takes less than a minute to set this up in an Excel spreadsheet .

You can also try to simplify the expression. What is the numerator?
 
  • #3
I don't really see how further I can simplyfy

numerator is

1 devided by ''b' minus 1 devided by 3
 
  • #4
Find the common factor.
 
  • #5
I don't see a common factor in

1/b - 1/3

or

b-3
 
  • #6
EvilBunny said:
(1/b) - (1/3)

How do you take the difference of two fractions?
 
  • #7
woa... nwo seriously how did I miss that. I wasted soo much time on this.
 
  • #8
well am still stuck.


So I put them on the same denominator and end with


(3-b) / 3 b
-------------
b-3
 
  • #9
okay -1/9 got it finally . thanks for the help
 

What is an annoying limit problem?

An annoying limit problem is a type of mathematical problem that involves finding the value of a limit as a variable approaches a certain value. These problems can be frustrating because they often require advanced math skills and can be difficult to solve.

Why are limit problems considered annoying?

Limit problems are considered annoying because they can be challenging to solve and often require multiple steps and advanced math techniques. Additionally, the answer to a limit problem may not always be intuitive or easy to understand.

Can limit problems be solved without using advanced math techniques?

While some limit problems can be solved using basic algebra and calculus, many problems require more advanced techniques such as L'Hopital's rule, series expansion, or trigonometric identities. It is important to have a strong understanding of these techniques in order to effectively solve limit problems.

What are some tips for solving annoying limit problems?

One helpful tip for solving limit problems is to first try to simplify the expression by factoring, canceling common terms, or using algebraic manipulation. It is also important to carefully analyze the given information and consider different approaches to the problem. Practice and familiarity with different types of limit problems can also make them less annoying.

Why are limit problems important in science?

Limit problems are important in science because they are used to model real-world situations and make predictions. For example, in physics, limit problems can be used to calculate the velocity of an object at a specific time or the rate of change of a chemical reaction. In biology, limit problems can be used to model population growth or the rate of enzyme reactions. Understanding and solving these problems is crucial for making accurate predictions and understanding scientific phenomena.

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