Answer:
1) the limit lim x→7 √[g(x) - f(x)] is equal to √6.
2) the limit lim x→8 [f(x) * g(x) - h(x)] is equal to 19.
Step-by-step explanation:
To evaluate the limit lim x→7 √[g(x) - f(x)], we can use the fact that the limit of a sum or difference is equal to the sum or difference of the limits. Additionally, the limit of a constant times a function is equal to the constant times the limit of the function.
Given:
lim x→7 f(x) = 2
lim x→7 g(x) = 8
Using the limit laws, we can rewrite the expression as follows:
lim x→7 √[g(x) - f(x)] = √[lim x→7 g(x) - lim x→7 f(x)]
Substituting the given values:
= √[8 - 2]
Simplifying further:
= √6
Therefore, the limit lim x→7 √[g(x) - f(x)] is equal to √6.
2.) To evaluate the limit lim x→8 [f(x) * g(x) - h(x)], we can again use the fact that the limit of a sum or difference is equal to the sum or difference of the limits, and the limit of a constant times a function is equal to the constant times the limit of the function.
Given:
lim x→8 f(x) = 4
lim x→8 g(x) = 6
lim x→8 h(x) = 5
Using the limit laws, we can rewrite the expression as follows:
lim x→8 [f(x) * g(x) - h(x)] = lim x→8 f(x) * lim x→8 g(x) - lim x→8 h(x)
Substituting the given values:
= 4 * 6 - 5
Simplifying further:
= 24 - 5
= 19
Therefore, the limit lim x→8 [f(x) * g(x) - h(x)] is equal to 19.
