Finding Constants for Continuity of Composite Function

  • Thread starter dylmans
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In summary, the conversation was about finding the constants a and b in a function in order to ensure continuity on the entire real line. The steps to finding these constants were also discussed, including solving simultaneous equations. The poster also asked about creating new threads for each new problem.
  • #1
dylmans
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Homework Statement


Find the constants a and b such that the function is continuous on the entire real line.


Homework Equations


f(x)={2, x< or = -1
{ax + b, -1<x<3
{-2, x> or = 3


The Attempt at a Solution


I don't know where to start.

If anyone is willing to help me with my calculus make up work let me know. I don't get it at all.
 
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  • #2
This isn't really calculus. You need to pick a and b so that a*(-1)+b=2 and a*(3)+b=-2. Do you see why?
 
  • #3
haha sorry it is in my calculus book. you i think i do. but how would you get a and b then?
 
  • #4
You would solve the two simultaneous equations -a+b=2 and 3a+b=(-2). I think that's in your algebra book.
 
  • #5
a=-1 and b=1, i don't have an algebra book but i got it somehow. do i need a new thread for each new problem i have?
 
  • #6
dylmans said:
a=-1 and b=1, i don't have an algebra book but i got it somehow. do i need a new thread for each new problem i have?

You don't have to. But you'll get better response time if you do. Posts with zero replies get much more attention.
 

1. What is the definition of continuity in composites?

Continuity in composites refers to the uninterrupted connection between the reinforcing fibers and the matrix material in a composite material. This ensures that the load transfer between the two materials is efficient and the overall strength and stiffness of the composite is maintained.

2. How does continuity affect the mechanical properties of composites?

Continuity plays a crucial role in determining the mechanical properties of composites. A lack of continuity can result in weak spots or discontinuities in the material, reducing its overall strength and stiffness. On the other hand, good continuity ensures efficient load transfer and can improve the strength and stiffness of composites.

3. What factors can disrupt the continuity of composites?

Several factors, such as voids, cracks, and interfacial debonding, can disrupt the continuity of composites. These defects can occur during the manufacturing process or as a result of external stresses on the material. It is important to minimize these disruptions to maintain the integrity of the composite structure.

4. How is continuity tested in composites?

The continuity of composites is typically tested through non-destructive techniques such as ultrasonic testing, X-ray imaging, and infrared thermography. These methods allow for the detection of any voids, cracks, or delamination within the material without causing damage.

5. How can continuity be improved in composites?

To improve the continuity of composites, proper manufacturing techniques and quality control measures should be implemented. This includes using high-quality materials, ensuring proper fiber orientation, and minimizing defects during the manufacturing process. Additionally, post-processing techniques such as resin infusion can also improve the continuity of composites.

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