Did i solved this limit correctly

[transgalactic]

$$lim_{x->\infty}\frac{3x-cosx}{4x+sinx}=lim_{x->\infty}\frac{\frac{3x-cosx}{x}}{\frac{4x+sinx}{x}}=lim_{x->\infty}\frac{3-0}{4-0}=0.75$$

i thought bounded/infinity=0


??

 

[Mark44]

You have the correct limit, but you should remove the limit operator from the expression below, since you have already "passed to the limit" in the previous expression:
$$lim_{x->\infty}\frac{3-0}{4-0}=0.75$$

 

[transgalactic]

thanks