Question

Evaluate the limit and justify each step by indicating theappropriate limit law

lim cos⁴x / 5 + 2x³

Answer 1

To evaluate the limit of (cos⁴x) / (5 + 2x³), substitute the value 0 for x and simplify the expression. The value of the limit is 1 / 5.

Step-by-step explanation:

To evaluate the limit of (cos⁴x) / (5 + 2x³), we can use the limit laws. Let's break down the steps:

1. First, substitute the value 0 for x in the expression. This will give us (cos⁴(0)) / (5 + 2(0)³).
2. Next, simplify the expression. Since cos⁴(0) = 1 and 0³ = 0, the expression becomes 1 / (5 + 0).
3. Lastly, complete the calculation. The value of the limit is 1 / 5.