1^infinity >= 1. 1) $$\displaystyle\lim_{x \to{+}\infty}{\Big(\frac{1}{1+x^2}\Big)^2x}=e^{\displaystyle\lim_{x \to{+}\infty}{\Big(\frac{1}{1+x^2}-1\Big) \cdot 2x}}=$$\$ Free Web Hosting with Unlimited Disk Space, Unlimited Bandwidth and Unlimited Websites from InfinityFree. Can't find the answer you're looking for or is an article unclear? 1^(-infinity) = 1/1^(infinity) 0 <= 1^(-infinity) <= 1. strictly speaking, 1 / infinity is infinitesimal (very small), and 1 / undefined is zero. Allí estaba, fría e inundada del halo azulado de la luz de estrellas difractada en el cianuro de la atmósfera: la Factoría, cuyos legendarios muros de piedra de basalto ocultaban el principio del misterio mejor guardado del Universo. for all practical purposes 1 / infinity = 0 ===== just thought of something! Compra Soundbar 2.1 Infinity 8 en Sodimac.cl, los mejores productos de Novik - 6112609. that is the language when talking about Pure Mathematics. x = .0000000000000000000001 aka an infinite number of 0's and then a 1??? With PHP and MySQL and no forced ads on your site. Well, n_kelthuzad's calculation is correct.You can substitute $b=\infty$ if You will, but the resulting equation makes no sense then. 1^infinity can have any positive value greater than or equal to 1. Un rumor profundo de viento milenario resonó entre las montañas amenazantes. That's because the limiting process is lost then, and one starts to calculate with $\infty$ as if $\infty$ was an ordinary finite number. Be sure to check our Community Forum as well! However, in applied sciences, where approximations are often prevalent, 1 / infinity is considered as zero, and the word "undefined" is seldom used. ok, start with 1 / infinity = x 1 = x * infinity ~~~~~ analyze this ^^ x must be a REALLY small number to get infinity back down to 1 i.e. or an infinite number of 0's and then a 2? Hi. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals.