## Continuity – Limits and Continuity

Continuity A function $$f(x)$$ is said to be continuous at a point $$a$$ in its domain if the following three properties hold. $$\displaystyle \lim_{x \to a} f(x)$$ exists. This takes three steps to show in itself. $$f(a)$$ has to exist, $$\displaystyle \lim_{x \to a} f(x) = f(a)$$. Continuity connects the behaviour of a function in … Read moreContinuity – Limits and Continuity

## Computing Limits II: The Squeeze Theorem – Application Proof

One very important application of the squeeze theorem is the proof that $$\displaystyle \lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$$. We present this proof next. This proof is for the limit as $$\theta\to 0^+$$. The case for $$\theta\to 0^-$$ can be proved in exactly the same manner and we leave it as an exercise to … Read moreComputing Limits II: The Squeeze Theorem – Application Proof