Finding f(x) Using Limit and Algebraic Manipulation

Thread starter tg43fly
Start date Sep 12, 2013
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Limit

In summary, the given limit of f(x)-8 / x-1 = 10 is solved by finding the limit of f(x) as x approaches 1, which is 8. The right hand side of the equation does not affect the solution, but can be used to find the limit of the first derivative of f(x).

Sep 15, 2013

Curious3141

Homework Helper

johnqwertyful said:

That's another way to do it, although I'm not sure if he cover l'hopitals.

I would comment that you don't know f is differentiable; but if it is differentiable, your last paragraph is cool.

There is no need to invoke L' Hopital's for the answer - that's just algebra.

I only used L' Hopital's Rule for the latter part ("for interest"), which is where the RHS would come into play. I should've stated that f(x) has to be differentiable around the neighbourhood of x = 1 for this to be valid.

<h2>1. What is the purpose of finding f(x) using limit and algebraic manipulation?</h2><p>The purpose of finding f(x) using limit and algebraic manipulation is to determine the value of a function at a specific point by using the concept of a limit. This method is useful when the function is not defined at that point or when it is difficult to evaluate the function directly.</p><h2>2. How do you find f(x) using limit and algebraic manipulation?</h2><p>To find f(x) using limit and algebraic manipulation, you first need to determine the limit of the function as x approaches the given point. Then, you can use algebraic manipulation techniques such as factoring, rationalizing, or simplifying to evaluate the limit and find the value of f(x).</p><h2>3. What are the common algebraic manipulation techniques used in finding f(x)?</h2><p>Some common algebraic manipulation techniques used in finding f(x) include factoring, rationalizing, simplifying, and using algebraic identities. These techniques help to simplify the expression and make it easier to evaluate the limit and find the value of f(x).</p><h2>4. When is it necessary to use limit and algebraic manipulation to find f(x)?</h2><p>It is necessary to use limit and algebraic manipulation to find f(x) when the function is not defined at the given point, or when it is difficult to evaluate the function directly. This method is also useful when the function is in an indeterminate form, such as 0/0 or ∞/∞, and cannot be evaluated using other methods.</p><h2>5. Can limit and algebraic manipulation always be used to find f(x)?</h2><p>No, limit and algebraic manipulation cannot always be used to find f(x). This method is only applicable when the limit of the function exists at the given point. If the limit does not exist, or if it is not possible to evaluate the limit using algebraic manipulation, then another method must be used to find the value of f(x).</p>

1. What is the purpose of finding f(x) using limit and algebraic manipulation?

The purpose of finding f(x) using limit and algebraic manipulation is to determine the value of a function at a specific point by using the concept of a limit. This method is useful when the function is not defined at that point or when it is difficult to evaluate the function directly.

2. How do you find f(x) using limit and algebraic manipulation?

To find f(x) using limit and algebraic manipulation, you first need to determine the limit of the function as x approaches the given point. Then, you can use algebraic manipulation techniques such as factoring, rationalizing, or simplifying to evaluate the limit and find the value of f(x).

3. What are the common algebraic manipulation techniques used in finding f(x)?

Some common algebraic manipulation techniques used in finding f(x) include factoring, rationalizing, simplifying, and using algebraic identities. These techniques help to simplify the expression and make it easier to evaluate the limit and find the value of f(x).

4. When is it necessary to use limit and algebraic manipulation to find f(x)?

It is necessary to use limit and algebraic manipulation to find f(x) when the function is not defined at the given point, or when it is difficult to evaluate the function directly. This method is also useful when the function is in an indeterminate form, such as 0/0 or ∞/∞, and cannot be evaluated using other methods.

5. Can limit and algebraic manipulation always be used to find f(x)?

No, limit and algebraic manipulation cannot always be used to find f(x). This method is only applicable when the limit of the function exists at the given point. If the limit does not exist, or if it is not possible to evaluate the limit using algebraic manipulation, then another method must be used to find the value of f(x).