# Introduction to Limits and Derivatives

Limits describe what one quantity approaches as some other quantity approaches a given value. This concept is the basis of calculus because it is used to define both derivatives and integrals. In this lesson, we'll try to wrap our minds around what the notion of a limit is and use it to define the derivative function.

# Proof of the Theorem: $$\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1$$

In this lesson, we’ll prove that $$\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1$$. We'll prove this result by using the squeeze theorem and basic geometry, algebra, and trigonometry. In a future lesson, we'll learn why this result is important: the reason being because knowledge that $$\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1$$ is required to find the derivatives of the sin and cosine functions. But we'll save that for a future lesson.