Question

find the limit
lim_(x,y)->(-30,6) xy cos(x + 5y)
(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:

\(-180\)