Which one of the following is correct regarding $\rm \lim\limits_{x\rightarrow 3}\frac{|x-3|}{x-3}$?

What is the maximum value of a cos x + b sin x + c? 

If f(2x) = 4x² + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?  

lf f(x) = [x]² - 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions?