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- Why does the limit as x goes to 0 of cos(1/x) not exist? Can use two different sequences: xn=1/(n*pi), and yn=2/((2n+1)pi) and show that lim cos(1/xn) ≠ lim cos(1/yn).Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the point (1, 2)? How do you know?if h(x) = coth-1(x) if x>=1 [[x+1]] if -1 < x < 1 tan-1 (x2+2x+1) if x<= -1 Is h continuous at x=-1, 0, and 1? If not, Is it removable, jump essential, or infinite?