Limit of a Ratio of Two Functions

In this post, I show that $\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x \rightarrow a}g(x)}$ given that $\lim_{x\rightarrow a}f(x)=A$, $\lim_{x \rightarrow a} g(x) = B$, $B \ne 0$ and $g(x) \ne 0$. To do this, I approximately…

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Limit of the Product of Two Functions

In this post, I show that $\lim_{x\rightarrow a}[f(x)g(x)] = \lim_{x\rightarrow a} f(x) \lim_{x\rightarrow a} g(x)$ given that $\lim_{x\rightarrow a} f(x) = A$ and $\lim_{x\rightarrow a} g(x) = B$. To do this, I approximately follow…

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Limit of a Difference of Two Functions

In this post, I show that $\lim_{x\rightarrow a}[f(x) – g(x)] = \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}…

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Limit of a Function Multiplied by a Scalar

In this post, I show that $ \lim_{x \rightarrow a} [c f(x)] = c \lim_{x \rightarrow a} [f(x)]$ if $c$ is a variable for any real number. To do this, I approximately follow the steps…

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