Question

Given that lim x→2 f(x) = 4 lim x→2 g(x) = −5 lim x→2 h(x) = 0,

find the limits, if they exist. (If an answer does not exist, enter DNE.)
(a) lim x→2 [f(x) + 4g(x)] (b) Lim x→2 [g(x)]³

Answer 1

To find the limits, use the given values and apply limit laws. The limit of f(x) + 4g(x) as x approaches 2 is -16, and the limit of [g(x)]³ as x approaches 2 is -125.

Step-by-step explanation:

The subject of the question is Mathematics, and it involves finding limits of functions. This is a typical problem in High School and early College calculus courses where students learn about the behavior of functions as the input values approach a certain point.

To find lim x→2 [f(x) + 4g(x)], you can use the provided limits:

• №f(x)№_2 = 4
• №g(x)№_2 = -5

Thus:

1. Add the limits of f(x) and 4 times g(x) as x approaches 2:
2. №[f(x) + 4g(x)]№_2 = №f(x)№_2 + 4(№g(x)№_2) = 4 + 4(-5) = 4 - 20 = -16.

For lim x→2 [g(x)]³, you raise the limit of g(x) as x approaches 2 to the power of 3.

• (№g(x)№_2)³ = (-5)³ = -125.