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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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Apply the property of the quotient of two powers with the same exponent, inversely: $\frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m$, where $m$ equals $2$
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$\lim_{x\to0}\left(\frac{\left(\frac{\sin\left(3x\right)}{x}\right)^2}{3}\right)$
Learn how to solve problems step by step online. Find the limit of (sin(3x)^2)/(3x^2) as x approaches 0. Apply the property of the quotient of two powers with the same exponent, inversely: \frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m, where m equals 2. The limit of the product of a function and a constant is equal to the limit of the function, times the constant. Example: \displaystyle\lim_{t\to 0}{\left(\frac{t}{2}\right)}=\lim_{t\to 0}{\left(\frac{1}{2}t\right)}=\frac{1}{2}\cdot\lim_{t\to 0}{\left(t\right)}. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. Apply the formula: \lim_{h\to0}\left(\frac{\sin\left(nh\right)}{h}\right)=n, where h=x and n=3.