cosine limits??

Question

lim x-> infinity (cos(5x/x^2+7 )+pi/3)

Will this be DNE because the cosine graph keeps oscillating from positive and negative?

Answer 1

lim_x→∞ [ cos ( 5x / (x²+7) ) + π/3 ] = cos0 + π/3 = 1 + π/3

Answer 2

This limit will not be DNE. The cosine graph does oscillate, and the limit of cos(x) as x approaches infinity is DNE, but in this case, 5x/x^2 will approach 0 as x approaches infinity, leaving you with cos(0+7) + pi/3

Also, make sure you formatted the parentheses properly in your question as that could affect the answer. Either way, the limit should exist.

Answer 3

Yes. DNE

unless f(x) approaches one real number as a limit there is no limit