What is the limit of a piecewise function with different equations at x=2?

[JessicaJ283782]

Homework Statement

Find the limit-> 2 g(x)= (x^2-3) if x < 2
3 if x=2
cos(x-2) if x>2

Homework Equations

So, I know you basically ignore the limit at 2, and you need to check it from the right and left. So, you want the x^2-3 and cos(x-2) equations

The Attempt at a Solution

I plugged two in for x, in both of these equations (2^2-3)=1 and cos(2-2)=cos(0)=1

So wouldn't the answer be 1?

 

[Dick]

Homework Statement

Find the limit-> 2 g(x)= (x^2-3) if x < 2
3 if x=2
cos(x-2) if x>2

Homework Equations

So, I know you basically ignore the limit at 2, and you need to check it from the right and left. So, you want the x^2-3 and cos(x-2) equations

The Attempt at a Solution

I plugged two in for x, in both of these equations (2^2-3)=1 and cos(2-2)=cos(0)=1

So wouldn't the answer be 1?

Yes, it would. Though you should be thinking 'the value of the functions approaches 1 as x->2' rather than saying 'I plugged in 2'.