You don't "pull the f out in front". ##f(x)## is the notation for a function of ##x##. Without knowing the formula defining ##f(x)## the problem can't be worked.chem_vo said:Homework Statement
Prove that the limit is 1 as x approaches 0 for the function f(x) / x.
Homework Equations
The Attempt at a Solution
I put the f out in front so I was left with f•Lim as (x → 0) (x/x) so I was left with f•lim(x→0) 1 so I used the limit property and was left with f•1. That was my attempt at proving however I have no idea how to prove it please help.
That's the only information we were given.LCKurtz said:You don't "pull the f out in front". ##f(x)## is the notation for a function of ##x##. Without knowing the formula defining ##f(x)## the problem can't be worked.
Yes I'm certain f(x) was never given.LCKurtz said:Then you can't work the problem. Are you certain that ##f(x)## wasn't defined earlier?
Yes I have studied functions I'm aware what a function is. That was the question given and I'm just trying to make sense of it.LCKurtz said:Have you studied functions? Do you understand the function notation such as ##f(x) = x^2## or some other formula? If so you should see that your problem is incompletely stated without knowing the formula.
The limit as x approaches 0 is a mathematical concept that represents the behavior of a function as its input (x) gets closer and closer to 0. It is denoted as lim x→0 f(x) and can be understood as the value that a function approaches as its input approaches 0.
Studying the limit as x approaches 0 can help us understand the behavior of a function near 0 and can provide insights into the overall behavior of the function. It is also an important concept in calculus and is used to solve various mathematical problems.
To calculate the limit as x approaches 0, you can use various mathematical techniques such as direct substitution, factoring, and algebraic manipulation. If these methods do not work, you can use the limit laws or L'Hôpital's rule to find the limit.
A one-sided limit as x approaches 0 only considers the behavior of a function as x approaches 0 from one side (either the positive or negative direction). A two-sided limit, on the other hand, considers the behavior of a function as x approaches 0 from both sides. In other words, a one-sided limit only looks at the function's behavior on one side of 0, while a two-sided limit looks at both sides.
The concept of limit as x approaches 0 has many real-world applications, such as calculating instantaneous rates of change, finding the slope of a tangent line, and determining the maximum and minimum values of a function. It is also used in physics, engineering, and economics to model and analyze real-world systems.