Find Values of c and f that make h continuous

  • Thread starter Painguy
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In summary, the conversation includes a discussion about finding the limit of a piecewise function and solving linear equations in two unknowns. The individual asking for help gets stuck after finding the two equations and is reminded that solving two linear equations in two unknowns is a basic concept. They then apologize for their mistake and thank the other person for their help.
  • #1
Painguy
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Homework Statement


{ 2x if x<1
h(x)= { cx^2+d if 1<=x<=2
{ 4x if x>2


Homework Equations





The Attempt at a Solution


It tried taking the limit of 2x and cx^2+d at x->1 (from both sides) and set them equal to each other. I did the same for 2 as well, but i got stuck after that.
 
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  • #2
What did you get after you did that??
 
  • #3
After evaluating those 2 i get 2=c+d and 8=4c+d. I'm not quite sure what to do now
 
  • #4
Painguy said:
After evaluating those 2 i get 2=c+d and 8=4c+d. I'm not quite sure what to do now

Are you saying that you do not know how to solve two simple linear equations in two unknowns? Have you really never, ever, seen problems like that before?

RGV
 
  • #5
Ray Vickson said:
Are you saying that you do not know how to solve two simple linear equations in two unknowns? Have you really never, ever, seen problems like that before?

RGV

OH well I am blind...excuse my stupidity thank you for your help
 

1. What is the purpose of finding the values of c and f that make h continuous?

The purpose of finding the values of c and f that make h continuous is to ensure that the function h(x) is smooth and has no breaks or gaps in its graph. This is important in many real-world applications, as discontinuous functions can lead to incorrect results and make the function difficult to work with.

2. How do I find the values of c and f that make h continuous?

To find the values of c and f that make h continuous, you can use the limit definition of continuity. This involves evaluating the left and right limits of h(x) at the point where the function is not continuous and equating them to the value of h(x) at that point. This will give you an equation that you can solve for c and f.

3. Can I use any value of c and f to make h continuous?

No, not all values of c and f will make h continuous. The values must satisfy the limit definition of continuity, which requires the left and right limits to be equal at the point of discontinuity. So, you will need to solve the equation derived from the limit definition to determine the specific values of c and f that make h continuous.

4. What happens if I cannot find values of c and f that make h continuous?

If you are unable to find values of c and f that make h continuous, it means that the function is not continuous at that point. This could be due to a variety of reasons, such as a removable or non-removable discontinuity, a jump or infinite discontinuity, or an oscillating function. In such cases, it is important to analyze the function further and consider the context of the problem to understand the behavior of h(x).

5. Are there any other methods for finding values of c and f that make h continuous?

Yes, there are other methods for finding values of c and f that make h continuous. One approach is to use the intermediate value theorem, which states that if a function is continuous on a closed interval, then it takes on every value between the function outputs at the endpoints of the interval. Another approach is to use graphical methods, such as plotting the function and visually determining the values of c and f that will make h continuous.

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