" Find the limit: " (lim)┬(x→-4^+ ) f(x)

Question

graph of the function f(x) = x^2 + 6 , x is not equal to -4 and f(x)=0 , x=-4

Answer 1

Since in the limit as x--> - 4⁺ you will approach the value -4 from the right, you can't use the definition f(x)=0 if x=-4.Instead you need to consider only the other part of the definition f(x)=x² + 6 because, in the process of limit, you will approach x=-4.

Hence, the limit will tend to (-4)² + 6 = 22 which is NOT the value of the function evaluated at x=-4. In fact f(-4)=0 while the limit as x-->-4⁺ is equal to 22.

If this is not clear, consider the value -3.99 which is close to -4⁺ . In this case x is not equal to -4 and hence you have (-3.99)^2+6=21.9201...

If you use -3.999 you will obtain (-3.999)^2 +6 =21.992....and you see that you're approaching the value 22 which is the correct limit (but not the value of the function at x=-4)

Best,

Davide