How to Find Constants for a Continuous Function?

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In summary, the problem is to find the constants a and b such that the function g(x) is continuous on the entire line, with a possible discontinuity at x=0. The given equations are g(x)={4 sinx/x, x<0} and {a-2x, x> or = 0}. There is some uncertainty about the value of f(0^-), but it can be determined that the limit of sinx/x as x approaches 0 is 1.
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dylmans
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Homework Statement


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


Homework Equations


g(x)={4 sinx/x, x<0
{a-2x, x> or = 0


The Attempt at a Solution


Possible discontinuity at x=0
f(0^+)=a-2x=a-2(0)=a
f(0^-)=4sinx/x=4sin(0)/(0)

i am stuck, wouldn't f(0^-) not exist then? i really don't know what I am doing on this entire assignment as i have been gone from school for a week so if anyone knows how to do this, I would love for you to help me on AIM or MSN tonight.
 
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  • #2
You seem to be doing fine, except you didn't know that the limit of sinx/x as x-->0 is 1. Now you know!
 

1. What is continuity of composites?

Continuity of composites refers to the degree to which the individual components of a composite material are connected or joined together. This connection is essential for the composite to function as a single, cohesive material.

2. Why is continuity important in composites?

Continuity is important in composites because it determines the strength and performance of the material. Without proper continuity, the composite may fail to meet its desired properties and may even fail completely.

3. How is continuity achieved in composites?

Continuity can be achieved in composites through various methods, such as using adhesives, interlocking fibers, or creating a chemical bond between the components. The specific method used depends on the type of composite and the desired properties.

4. What factors can affect the continuity of composites?

Several factors can affect the continuity of composites, including the type and quality of the bonding material, the manufacturing process, and external stresses or forces on the material.

5. How does continuity impact the design of composites?

The level of continuity in a composite material can greatly impact its design. In some cases, a higher level of continuity may be desired for increased strength and durability, while in other cases, a lower level of continuity may be preferred for flexibility or other properties.

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