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Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
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$\lim_{x\to0}\left(\csc\left(3x\right)^2+\frac{-1}{x^2}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of 1/(sin(3x)^2)-1/(x^2) as x approaches 0. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Combine \csc\left(3x\right)^2+\frac{-1}{x^2} in a single fraction. Evaluate the limit \lim_{x\to0}\left(\frac{-1+x^2\csc\left(3x\right)^2}{x^2}\right) by replacing all occurrences of x by 0. Multiply 3 times 0.