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tg43fly
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Homework Statement
lin x-> 1
f(x)-8 / x-1 = 10
find f(x)
Homework Equations
The Attempt at a Solution
i don't know where to start on finding f(x), i assume it includes (x-1) to eliminate the 0 denominator, i need some hints
tg43fly said:would this also address the 0 denominator given lim x->1 for (x-1)?
f(x) * g(x) = 10x-2
would this be on the right path?
tg43fly said:lim x->1 (f(x)-8)(g(x)) / (x-1) = 10*g(x)
so i have to find g(x) which is a constant?
tg43fly said:would lim x->1 g(x) = 8?
lendav_rott said:Whoah, I'm interested in this one too now.
If lim x->1 g(x) = c what do you mean by "what g(x) would simplify things" in the product of the 2 limits?
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.
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).
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).
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.
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).