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education/math/MATH1210 (calc 1)/Limits.md
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@ -30,7 +30,9 @@ $$ \lim_{x \to a^*} \frac{f(x)}{g(x)} = \infty \space or \space \lim_{x \to a^*}
# Limits of the Form $\frac{\infty}{\infty}$ # Limits of the Form $\frac{\infty}{\infty}$
If we have a limit of the form $\lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to \infty$ and $g(x) \to \infty$ as $x \to a$ then the limit may or may not exist and is said to be an indeterminate form of type $\frac{\infty}{\infty}$. If we have a limit of the form $\lim_{x \to a} \frac{f(x)}{g(x)}$ where both $f(x) \to \infty$ and $g(x) \to \infty$ as $x \to a$ then the limit may or may not exist and is said to be an indeterminate form of type $\frac{\infty}{\infty}$.
To find the limit if it exists we must perform some algebraic manipulations on the quotient in To find the limit if it exists we must perform some algebraic manipulations on the quotient in order to change the form of the function.
If $f(x)$ and $g(x)$ are polynomials, then we can multiply the numerator and denominator by $\dfrac{1}{x^n}$, where $n$ is the degree of the polynomial in the denominator.
# Continuity # Continuity
A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page. A function is continuous if their graph can be traced with a pencil without lifting the pencil from the page.