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education/math/MATH1210 (calc 1)/Limits.md
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@ -25,7 +25,8 @@ To find this limit if it exists we must perform some mathematical manipulations
- Combine fractions in the numerator or denominator of a complex fraction - Combine fractions in the numerator or denominator of a complex fraction
# Limits of the Form $\frac{k}{0}, k \ne 0$ # Limits of the Form $\frac{k}{0}, k \ne 0$
If we have a one sided limit of the form $\lim_{x \to a^*} \frac{f(x)}{g(x)}$ If we have a one sided limit of the form $\lim_{x \to a^*} \frac{f(x)}{g(x)}$ $f(x) \to k (k \ne 0)$ and $g(x) \to 0$ as $x \to a$ then:
$$ \lim_{x \to a^*} \frac{f(x)}{g(x)} = \infty \space or \space \lim_{x \to a^*} \frac{f(x)}{g(x)} = -\infty $$
# 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.