Question

Find the numerical value for W such that L'Hopital's Rule applies to the following limit, then compute value L of that limit.

limx→9 (4x^2-27x+w)/(x-9)

Answer 1

For L'Hopital's rule to apply 4x^2 - 27x + w = x - 9 = 0
x = 9
4(9)^2 - 27(9) + w = 0
4(81) - 243 + w = 0
81 + w = 0
w = -81

L = limx→9 (4x^2 - 27x -81)/(x - 9) = limx→9 (8x - 27) = 8(9) - 27 = 72 - 27 = 45.
L = 45