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Proceeding from the definiton of the limit of a function after Cauchy (ie, in the term of e-deltal e-M'' etc). Prove that (a) underset(x to 1)lim (3x-8)=-5, (b) underset(x to oo)lim (5x+1)/(3x+9)=5/3 (c) underset(x to 1)lim (1)/((1-x)^(2))=+oo, (d) underset(x to oo)lim log_(a) x=oo (a gt 1), (e) underset( x to oo)lim arc tan x=pi/2, (f) underset(x to pi/6) sin x=1/2 |
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