How Do I Solve This Limit Using Factoring X Out?

In summary, the conversation discusses finding the limit of a function and solving a polynomial equation using a specific strategy. The method involves factoring and using polynomial division to evaluate the limit. This approach is similar to one previously advised and is considered to be a useful and effective method.
  • #1
quasar987
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I Have No Clue How To Start This One. I Tried Applying The Same Kind Of Strategy As In https://www.physicsforums.com/showthread.php?t=51562 But No Luck. Please Give Me A Hint.

[tex] \lim_{x\rightarrow 0}\frac{\sqrt[4]{1+x^2}-1}{x} [/tex]

Factoring X Out Gives A [itex]\infty - \infty[/itex] Undeterminate Form. The answer is 0.
 
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  • #2
Set:
[tex]a=\sqrt[4]{1+x^{2}}, b=1^{\frac{1}{4}}=1[/tex]
Find the polynomial in a, b P(a,b) which satisfies:
[tex](a-b)P(a,b)=a^{4}-b^{4}[/tex]
In order to find P(a,b), use polynomial division on:
[tex](a^{4}-b^{4}):(a-b)[/tex]

In order then to evaluate the limit, multiply your fraction with:
[tex]1=\frac{P(a,b)}{P(a,b)}[/tex]
 
  • #3
Simply amazing!

And I realize this method is the same as the one which have been advised to me for the other limit problem, but generalized. Thanks arildno !
 

What is factoring X out limit?

Factoring X out limit is a mathematical technique used to simplify algebraic expressions by finding a common factor and factoring it out. This is commonly used in calculus to evaluate limits.

What is the process of factoring X out limit?

The process involves identifying the common factor, factoring it out, and then evaluating the limit. This can be done by dividing both the numerator and denominator by the common factor and then taking the limit as the common factor approaches zero.

When is factoring X out limit used?

Factoring X out limit is used in calculus to evaluate limits of algebraic functions. It is particularly useful when the expression contains a variable in the denominator, making it difficult to evaluate the limit directly.

What are the benefits of factoring X out limit?

Factoring X out limit allows for simplification of algebraic expressions, making them easier to evaluate and understand. It can also help in finding the domain of a function and identifying any vertical asymptotes.

Are there any limitations to factoring X out limit?

While factoring X out limit is a useful technique, it may not always work for more complex expressions. In some cases, other methods such as L'Hôpital's rule may be needed to evaluate the limit. Additionally, it is important to check for any restrictions on the variable that may affect the limit.

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