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Author: Tinku Tara

show-that-the-improper-integral-lim-B-0-B-sin-x-sin-x-2-dx-converges-

Question Number 150994 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\underset{{B}\rightarrow\infty} {\mathrm{lim}}\:\:\int_{\mathrm{0}} ^{\:{B}} \:\mathrm{sin}\left({x}\right)\mathrm{sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$\:\: \\ $$$$\:\:\:\mathrm{converges} \\…

lim-n-n-0-sin-x-n-dx-

Question Number 19920 by lidaye last updated on 18/Aug/17 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{n}\int_{\mathrm{0}} ^{\infty} \mathrm{sin}\:{x}^{{n}} \mathrm{d}{x} \\ $$ Commented by 1kanika# last updated on 18/Aug/17 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\mathrm{this}\:\mathrm{question}? \\…

Question-19915

Question Number 19915 by ajfour last updated on 18/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Four}\:{equal}\:{spheres}\:{of}\:{radius}\:{r} \\ $$$${are}\:{externally}\:{tangent}\:{to}\:{the}\:{three} \\ $$$${others}.\:{Find}\:{the}\:{radius}\:{of}\:{a}\:{sphere} \\ $$$${tangent}\:{to}\:{all}\:{four}\:{spheres}\:{and} \\ $$$${containing}\:{them}\:{within}\:{it}.…

Question-19912

Question Number 19912 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Find}\:{tangent}\:{of}\:{the}\:{acute}\:{angle} \\ $$$${between}\:{AB}\:{and}\:{SC}\:{and}\:{the} \\ $$$${shortest}\:{distance}\:{between}\:{them}. \\ $$$${The}\:{side}\:{of}\:{the}\:{equilateral}\:{triangle} \\ $$$${is}\:{even}\:\boldsymbol{{a}}.\:{SA}\:{is}\:{perpendicular}\:{to}…