How do I know which function to consider to get this limit?

[bushra1175]

Hi everyone. Here is the question:

Here is the function:

I underatand that I need to work out the limit as x tends to 0 from the right, but all the functions cover values from the right of 0 so which function is the correct one?

 

[pka]

Can you tell us the value of \(f(0)\) and why?

 

[bushra1175]

Can you tell us the value of \(f(0)\) and why?

for f(0) I'd have to use the function 2x+1 because x<3, which equals 1.
However, if we're getting the limit as x tends to 0 from the right side, meaning all values greater than 0, it would also satisfy the other functions as well? no?

 

[pka]

Well done! Now \(x\approx 0\) but \(x>0\) then \(f(x)\approx~?\)

 

[bushra1175]

Well done! Now \(x\approx 0\) but \(x>0\) then \(f(x)\approx~?\)

is it 1?

 

[pka]

is it 1?

So \(\mathop {\lim }\limits_{x \to {0^ + }} f(x) = 1\)

 

[Dr.Peterson]

Hi everyone. Here is the question: View attachment 21627

Here is the function: View attachment 21628

I understand that I need to work out the limit as x tends to 0 from the right, but all the functions cover values from the right of 0 so which function is the correct one?

The key idea is that the limit cares only about points near 0. Yes, as you approach 0 from far away, you will pass through the other regions, but you will then stay within the first region, and that is all that matters. Check the definition and see why.