Finding the value of constants in f(x) as x->0

In summary, the conversation is about finding the values of constants a and b in a limit problem. The person is having trouble solving it and has attempted different methods, including using the limit property. They are unsure of where to start and whether to solve for a variable or use trial-and-error.
  • #1
XenoWolf
1
0
I'm not looking for the complete answer (from what I've read in the intro posts, you won't/shouldn't give it to me anyways)... I just need to figure out where to start. This is my first time taking calc, and I'm pretty lost. Thanks in advance.

Homework Statement



Find the values of the constants a and b such that

lim (x[tex]\rightarrow[/tex]0) [ ( [tex]\sqrt{a+bx}[/tex] - [tex]\sqrt{3}[/tex] ) / x ] = [tex]\sqrt{3}[/tex]

The Attempt at a Solution



I've attempted to solve it a couple of ways in an algebraic style, but the fact that there are three 'variables' has me stumped. I also tried using the limit property that states the limit of h(x)=f(x)/g(x) as x->c is L/K (I hope I got that right.. hah.) but the fact that K ends up being zero screws that up...

I'm just completely lost as to where I need to start the problem. I don't know if I should be solving for a variable, doing trial-and-error stuff, using some kind of limit property, etc.
 
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  • #2
Let
[tex]f(x)=\frac{\sqrt{a+b\,x}-\sqrt3}{x}=\frac{g(x)}{x}[/tex]
and solve for [itex]g(x)[/itex]

What's the limit [tex]\lim_{x\to 0}g(x)[/tex] ?
 

1. What is the significance of finding the value of constants in f(x) as x->0?

Finding the value of constants in a function as x approaches 0 allows us to understand the behavior of the function at the origin, which can provide valuable insights into the overall behavior of the function.

2. How do you determine the value of a constant in this scenario?

The value of a constant can be determined by evaluating the function at x=0 and solving for the constant. This can be done algebraically or by using graphing tools.

3. Can the value of a constant in f(x) as x->0 be negative?

Yes, the value of a constant in this scenario can be negative. It all depends on the function and its behavior at the origin.

4. What is the practical application of finding the value of constants in f(x) as x->0?

Finding the value of constants can have practical applications in various fields such as physics, engineering, and economics. It can help in predicting the behavior of a system or evaluating the accuracy of a mathematical model.

5. Are there any limitations to finding the value of constants in this scenario?

One limitation is that the function may not be defined for x=0, which would make it impossible to find the value of a constant. Additionally, this method may not work for more complex functions with multiple variables or variables approaching a different value.

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