Question

Consider the function f(x) = sin(x)/x. Determine the limit of f(x) as x approaches 0.

a) 0
b) 1
c) -1
d) Does not exist

Answer 1

The limit of the function f(x) = sin(x)/x as x approaches 0 is a special case known in calculus and evaluates to 1, which means the correct option is b) 1.

Step-by-step explanation:

The student asked to find the limit of the function f(x) = sin(x)/x as x approaches 0. This is a well-known limit in calculus and is often approached by applying L'Hôpital's Rule. However, this limit can also be evaluated by recognizing it as a special limit that occurs frequently in mathematical analysis. The limit of sin(x)/x as x approaches 0 is 1. This can also be understood geometrically, as the values of sin(x) get closer and closer to x itself when x approaches 0, making the ratio approach 1. Therefore, we can provide correct option in the final answer, which is option b) 1.