Final answer:
The question asks to solve the limit of (sin x / x) as x approaches 0, which is known to be 1. Small angle approximations for trigonometric functions are relevant to solving similar limit problems in calculus.
Step-by-step explanation:
The student is asking for the solution to a limit in mathematics, specifically the limit of the expression (sin x / x) as x approaches 0, which is a common limit problem in calculus. For small angles expressed in radians, sin x is approximately equal to x, which can be used to simplify the problem. However, the limit as x approaches 0 of sin x / x is a foundational limit in calculus known to equal 1, and it can be proved using L'Hospital's Rule or geometric arguments involving the unit circle.
It's important to note that there are several approximations that relate to trigonometric functions like sin, tan, and cos when considering small angles. For instance, tan θ is approximately equal to sin θ, which is also approximately equal to θ.