Limit of a Sum of Two Functions

In this post, I show that $ \lim_{x \rightarrow a} [f(x) + g(x)]$ is equal to $\lim_{x \rightarrow a}f(x) + \lim_{x \rightarrow a} g(x)$ given that $ \lim_{x \rightarrow a}f(x) = A$ and $ \lim_{x \rightarrow a}g(x) = B$. To do this, I approximately follow the steps in Reference [1]. Objective: Using the definition of a limit, the objective is …

Limit of a Sum of Two Functions Read More »

Limit of a Constant

In this post, I prove that $ \displaystyle \lim_{x \rightarrow a} c = c $ if $c$ is a variable for any real number. To do this, I approximately follow the outline from reference [1]. Essential Background Information: Definition of a Limit: A function $f(x)$ approaches a limit $A$ as $x$ approaches $a$ if, and only …

Limit of a Constant Read More »

Do the angle addition identities only work for positive angles?

The Angle Addition Identities were derived using $\sin\theta \equiv \frac{opp}{hyp}$ and $\cos\theta \equiv \frac{adj}{hyp}$. In addition, $\theta$ was constrained to the interval of $[0, \frac{\pi}{2})$. The question addressed in this post is, do the Angle Addition Identities work if the arguments of the sine function and cosine functions are generalized to include negative numbers? In the following, …

Do the angle addition identities only work for positive angles? Read More »