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Author: Tinku Tara

lim-x-0-1-tan-1-3x-1-3-1-sin-1-3x-1-3-1-sin-1-2x-1-tan-1-2x-

Question Number 153449 by liberty last updated on 07/Sep/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3}{x}\right)}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{3}{x}\right)}}{\:\sqrt{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}−\sqrt{\mathrm{1}+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)}}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

For-each-positive-integer-n-define-a-n-20-n-2-and-d-n-gcd-a-n-a-n-1-Find-the-set-of-all-values-that-are-taken-by-d-n-and-show-by-examples-that-each-of-these-values-are-attained-

Question Number 22379 by Tinkutara last updated on 16/Oct/17 $$\mathrm{For}\:\mathrm{each}\:\mathrm{positive}\:\mathrm{integer}\:{n},\:\mathrm{define}\:{a}_{{n}} \:= \\ $$$$\mathrm{20}\:+\:{n}^{\mathrm{2}} ,\:\mathrm{and}\:{d}_{{n}} \:=\:{gcd}\left({a}_{{n}} ,\:{a}_{{n}+\mathrm{1}} \right).\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{values}\:\mathrm{that}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{by} \\ $$$${d}_{{n}} \:\mathrm{and}\:\mathrm{show}\:\mathrm{by}\:\mathrm{examples}\:\mathrm{that}\:\mathrm{each}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{values}\:\mathrm{are}\:\mathrm{attained}. \\…

Question-87911

Question Number 87911 by jagoll last updated on 07/Apr/20 Commented by jagoll last updated on 07/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{W}. \\ $$$$\mathrm{i}\:\mathrm{forgot}\:\mathrm{your}\:\mathrm{method}. \\ $$$$\mathrm{please}\:\mathrm{remember}\:\mathrm{me}\:\mathrm{for}\:\mathrm{this}\: \\ $$$$\mathrm{question} \\ $$…

L-1-s-s-2-12s-40-

Question Number 153446 by mathdanisur last updated on 07/Sep/21 $$\mathrm{L}^{−\mathrm{1}} \left\{\frac{\mathrm{s}}{\mathrm{s}^{\mathrm{2}} \:-\:\mathrm{12s}\:+\:\mathrm{40}}\right\}\:=\:? \\ $$ Commented by alisiao last updated on 07/Sep/21 $$=\:{L}^{−\mathrm{1}} \:\left\{\frac{\left({s}−\mathrm{6}\right)}{\left({s}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{4}}\:+\:\frac{\mathrm{6}}{\left({s}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{4}}\right\}…