Final answer:
The limit of 3x/cos(x) as x approaches 0 is 0. By directly substituting 0 into the given expression, the result simplifies to 0, making option a) the correct choice.
Step-by-step explanation:
The task is to find the limit of the expression 3x/cos(x) as x approaches 0. To solve this, we can apply direct substitution since cos(0) is a defined value, and we do not encounter an indeterminate form. At x = 0, cos(0) equals 1. Therefore, by directly substituting 0 into the expression, we get 3*0/1, which simplifies to 0. Hence, the limit of 3x/cos(x) as x approaches 0 is 0.
Therefore, when given the options:
- a) 0
- b) 3
- c) -3
- d) Undefined
The correct option for the final answer is a) 0.