find the limit\nlim_(x,y)->(-30,6) xy cos(x + 5y)\n(enter dne if the limit does not exist)

Explanation:

Step1: Substitute values

Substitute (x=-30) and (y = 6) into (xy\cos(x + 5y)). [(-30)\times6\times\cos(-30+5\times6)]

Step2: Simplify the argument of cosine

Calculate (-30 + 5\times6=-30 + 30=0). So we have ((-30)\times6\times\cos(0)).

Step3: Evaluate cosine and multiply

Since (\cos(0)=1), then ((-30)\times6\times1=- 180).

Answer:

(-180)