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)

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

You can find the area of a rectangle by multiplying the length and height. so multiply 1/2*7/4(which is the simpler version of 1 3/4) and you get 7/8 as your answer.