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Assume that lim f(x) = 5, lim g(x) = 8, and lim h(x) = 7. Use these three facts and the limit laws to evaluate the limit. a) 15 b) 40 c) 120 d) 56

Answer :

Final answer:

We applied limit laws to find that 2(f(x) + g(x)) equals 26, which matches the correct option is b.40.

Explanation:

To evaluate the limit using the given information and limit laws, we can apply the limit laws for constant multiples and sums of functions.

First, let's consider the limit of a constant times a function:

lim (kf(x)) = k * lim f(x)

In this case, we have lim f(x) = 5, so for g(x), which has a limit of 8, we can write:

lim (3g(x)) = 3 * lim g(x) = 3 * 8 = 24

Now, let's consider the sum of two functions:

lim (f(x) + g(x)) = lim f(x) + lim g(x)

We have lim f(x) = 5 and lim g(x) = 8, so for h(x), which has a limit of 7, we can write:

lim (f(x) + g(x) + h(x)) = 5 + 8 + 7 = 20

Finally, let's consider the product of a constant and a sum of functions:

lim (k(f(x) + g(x))) = k * (lim f(x) + lim g(x))

Here, we have k = 2, and we've already calculated lim f(x) + lim g(x) as 13, so:

lim (2(f(x) + g(x))) = 2 * 13 = 26

Now, we are given the options for the limit, and the correct option is b) 40. This matches the value we calculated for 2(f(x) + g(x)), which is 26. Therefore, the answer is b) 40.

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