Question

Given that

lim x→1 f(x) = 1
lim x→1 g(x) = −2
lim x→1 h(x) = 0,
find the limits, if they exist. (If an answer does not exist, enter DNE.)

lim x→1 [f(x) + 3g(x)]

Answer 1

The limit of the expression lim x→1 [f(x) + 3g(x)] is -5.

Step-by-step explanation:

To find the limit of the expression limx→1 [f(x) + 3g(x)], we can use the limit properties. According to the properties of limits, the limit of a sum of two functions is equal to the sum of their individual limits. Therefore, we can rewrite the expression as limx→1 f(x) + limx→1 (3g(x)).

Substituting the given limit values, we have 1 + 3(-2) = 1 - 6 = -5.

Therefore, the limit of limx→1 [f(x) + 3g(x)] is -5