How Do You Find the Limit of A(z) as z Approaches 3?

In summary, the limit of the function A(z) as z approaches 3 is 1. This is achieved by factoring the numerator and denominator to cancel out the (z-3) term.
  • #1
coolbeans33
23
0
A(z)= 2z-6/ z2-5z+6

find the limit as z-->3

I factored the denominator to get (z-2)(z-3), and manipulated the function to get:

2z2-62/(z-2)(z-3)(2z+6)

but I'm just not sure what to do in order to get rid of the (z-3)

I hope there's some obvious answer that I'm not seeing!
 
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  • #2
coolbeans33 said:
A(z)= 2z-6/ z2-5z+6

find the limit as z-->3

I factored the denominator to get (z-2)(z-3), and manipulated the function to get:

2z2-62/(z-2)(z-3)(2z+6)

but I'm just not sure what to do in order to get rid of the (z-3)

I hope there's some obvious answer that I'm not seeing!

You can factor the numerator to \(\displaystyle 2(z-3)\). Since z never reaches 3 you can cancel \(\displaystyle x-3\)
 

FAQ: How Do You Find the Limit of A(z) as z Approaches 3?

What is the purpose of finding the limit of a function?

The limit of a function tells us the value that the function approaches as the input approaches a certain value. It helps us understand the behavior of the function and make predictions about its values.

How do you find the limit of a function?

To find the limit of a function, we evaluate the function at values closer and closer to the input value. If the function approaches a specific value, then that value is the limit. If the function approaches different values from the left and right sides, the limit does not exist.

What does it mean if the limit of a function does not exist?

If the limit of a function does not exist, it means that the function does not approach a specific value as the input approaches a certain value. This could be due to a jump, a vertical asymptote, or oscillation of the function.

Can a function have more than one limit?

Yes, a function can have more than one limit. This occurs when the function approaches different values from the left and right sides of the input value. In this case, the limit does not exist.

What are the different types of limits of a function?

The different types of limits of a function include: finite limits, infinite limits, and limits at infinity. Finite limits occur when the function approaches a specific value. Infinite limits occur when the function approaches positive or negative infinity. Limits at infinity occur when the function approaches a specific value as the input approaches positive or negative infinity.

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