I need help guys

sin(3x - 12)  / (x - 4)     as x →  4

We have a  0/0   situation, here....so we can use L'Hospital's Rule

Taking the derivative with respect to x on top/bottom, we have

3cos(3x - 12)      as  x  →  4  =

3cos(3(4) - 12)  =

3cos(12 - 12)  =

3cos(0)   =

3 * 1  =

3

This graph confirms the results :   https://www.desmos.com/calculator/60evrkvzkx

i want to fint the lim of this Lim-->4  sin(3x-12)/x-4              and plz explain me how you find it! 

Find the following limit:
lim_(x->(-(4 sin(12-3 x))/x)^-) 4

Since 4 is constant, lim_(x->(-(4 sin(12-3 x))/x)^-) 4  =  4:
Answer: | =4

Find the following limit: Limit from opposite direction:
lim_(x->(-(4 sin(12-3 x))/x)^-) 4

Since 4 is constant, lim_(x->(-(4 sin(12-3 x))/x)^-) 4  =  4:
Answer: | =4

THIS IS TRUE ONLY IF THE DENOMINATOR IS: x - 4 AND NOT (x - 4).

Can also be done as follows:

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