Question

You are given that lim f(x) = -3, lim g(x) = -4, and lim h(x) = 2. Find the limit lim{[h(x)]^2 - f(x)g(x)}. A. 17 B. -8 C. 0 D. 22

Answer 1

Explanation:

To find the limit of the expression lim{[h(x)]^2 - f(x)g(x)}, you can use the limit properties:

lim{[h(x)]^2 - f(x)g(x)} = [lim{h(x)}]^2 - [lim{f(x)}][lim{g(x)}]

Given:

lim{h(x)} = 2

lim{f(x)} = -3

lim{g(x)} = -4

Now, substitute these values into the expression:

[lim{h(x)}]^2 - [lim{f(x)}][lim{g(x)}] = (2)^2 - (-3)(-4)

Simplify the expression:

4 - 12 = -8

So, the limit of the expression lim{[h(x)]^2 - f(x)g(x)} is:

B) -8