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Let x=a+d where d is a very small positive or negative number much smaller than x. Put x=a+d into the limit expression: x^2-a^2=(x-a)(x+a)=d(2a+d)=2ad, if we ignore d^2 as being too small. sin(3x-3a)=sin(3d)=3d when d is very small. So the limit expression is 2ad/3d=2a/3. This is the result of applying the limit as d approaches zero, so x approaches a. If the limit is 4 then 2a/3=4 and a=3/2*4=6. So the limit is 6.

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