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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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Factor the trinomial $x^2-5x+6$ finding two numbers that multiply to form $6$ and added form $-5$
Learn how to solve limits by direct substitution problems step by step online.
$\begin{matrix}\left(-2\right)\left(-3\right)=6\\ \left(-2\right)+\left(-3\right)=-5\end{matrix}$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of (x^2-9)/(x^2-5x+6) as x approaches 3. Factor the trinomial x^2-5x+6 finding two numbers that multiply to form 6 and added form -5. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. If we directly evaluate the limit \lim_{x\to3}\left(\frac{x^2-9}{\left(x-2\right)\left(x-3\right)}\right) as x tends to 3, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.
