Question

What is the limit as x approaches 0 of (sin^2(x) / x)?

A) 0
B) 1
C) -1
D) Undefined

Answer 1

The limit of sin^2(x) / x as x approaches 0 is 0, because sin(x) approaches 0 and the limit of sin(x)/x is 1 as x approaches 0.

Step-by-step explanation:

The question is asking about the limit of the function sin2(x) / x as x approaches 0. We can approach this problem by noting that the limit of sin(x)/x as x approaches 0 is a well-known limit in calculus, and it equals 1.

To find the limit of sin2(x) / x, we can rewrite it as (sin(x)/x) * sin(x). As x approaches 0, sin(x) approaches 0, and we already established that sin(x)/x approaches 1. Thus, the limit is:

(sin(x)/x) * sin(x) = 1 * 0 = 0

So, the correct answer is A) 0.