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- Homework Statement
- Find the limit as x approaches 0 x^2/(sin(^2)x(9x))

- Relevant Equations
- limit as x approaches 0 x^2/(sin(^2)x(9x))

Find the limit as x approaches 0 of x

I thought I could break it up into:

limit as x approaches 0 ((x)(x))/((sinx)(sinx)(9x)).

So that I could get:

lim

I would then get 1 ⋅ 1 ⋅ 1/0. Meaning it would not exist.

However the solution is 1/81 in the textbook, would this mean I would have to multiply the numerator and denominator, specifically 1/9x by x/x to get x/9x

Thank you.

^{2}/(sin^{2}x(9x))I thought I could break it up into:

limit as x approaches 0 ((x)(x))/((sinx)(sinx)(9x)).

So that I could get:

lim

_{x→0}x/sinx ⋅ lim_{x→0}x/sinx ⋅ lim_{x→0}1/9x.I would then get 1 ⋅ 1 ⋅ 1/0. Meaning it would not exist.

However the solution is 1/81 in the textbook, would this mean I would have to multiply the numerator and denominator, specifically 1/9x by x/x to get x/9x

^{2}. If so, why would I have to do this? If this is wrong how would I approach this then?Thank you.