Homework equations the attempt at a solution is it because it never stops continuing to infinity It just oscilates until 1 And does sinx also diverge I was playing around with infinity, and entered cos (infinity), which returned sin (infinity) The discussion centers on determining the limits of the expressions involving cos (nπ) and sin (nπ) as n approaches infinity This isn't homework just wanted to know what the values are
The discussion focuses on proving that the limit of cos (1/x) as x approaches 0 does not exist It is emphasized that since cos (x) oscillates and does not converge to a single value as x approaches infinity, the limit cannot exist A key point is that. The integral of cos (x^2) cannot be expressed in terms of elementary functions, but specific values can be evaluated, such as the definite integral from 0 to infinity, which equals (1/2)√ (π/2) The discussion highlights the use of complex analysis and contour integration to derive this result Participants also explore the possibility of using series expansion for approximations and.
The discussion emphasizes the importance of the formal definition of limits, highlighting that for any proposed limit l, there exists an epsilon such that the integral cannot get arbitrarily close to l for all x greater than some m. The computation you did somehow got the inequalities mixed up Questioning things this way is very good It forces you to get things absolutely clear, rather than half understanding.
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