Question

If we define:
L(α)=limx→αx²+8x+kx+2
If α=−2 the limit exists provided k=12⇒L(−2)=4

Answer 1

To find the value of L(-2) in the given function, we substitute the given values of α and k and evaluate the function at x = -2. The calculated value is 4.

Step-by-step explanation:

We are given α = -2, so the limit L(α) exists if k = 12. We want to find L(-2) which is equal to the limit of the function as x approaches -2.

Substituting α = -2 and k = 12 into the function, we have:

L(-2) = limx→-2x²+8x+kx+2 = limx→-2x²+8x+12x+2 = limx→-2x²+20x+2

Now, substituting x = -2 into the function, we have:

L(-2) = (-2)²+20(-2)+2 = 4