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Question-105266

Question Number 105266 by mohammad17 last updated on 27/Jul/20 Answered by mathmax by abdo last updated on 27/Jul/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{L}\left(\mathrm{t}^{\frac{\mathrm{3}}{\mathrm{2}}} \right)\:=\int_{\mathrm{0}} ^{\infty} \:\mathrm{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \:\mathrm{e}^{−\mathrm{tx}} \mathrm{dx}\:=_{\mathrm{tx}\:=\mathrm{u}} \:\:\int_{\mathrm{0}}…

Prove-that-for-any-real-number-x-and-odd-positive-integer-n-cos-n-x-1-2-n-1-k-0-n-1-2-C-k-n-cos-n-2k-x-

Question Number 170800 by thfchristopher last updated on 31/May/22 $$\mathrm{Prove}\:\mathrm{that},\:\mathrm{for}\:\mathrm{any}\:\mathrm{real}\:\mathrm{number}\:{x}\:\mathrm{and}\:\mathrm{odd}\:\mathrm{positive}\:\mathrm{integer}\:{n}, \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}^{{n}} {x}=\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\underset{{k}=\mathrm{0}} {\overset{\left({n}−\mathrm{1}\right)/\mathrm{2}} {\sum}}{C}_{{k}} ^{{n}} \mathrm{cos}\:\left({n}−\mathrm{2}{k}\right){x} \\ $$ Answered by aleks041103 last updated…

Question-170796

Question Number 170796 by Beginner last updated on 31/May/22 Answered by som(math1967) last updated on 31/May/22 $$\left[\frac{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \left\{\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \right\}}{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \left\{\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \right\}}\right]^{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}} \\ $$$$\left(\sqrt{\mathrm{2}}\right)^{\frac{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}}…

1-1-3-2-1-3-5-3-1-3-5-7-n-terms-Find-sum-

Question Number 105250 by bshahid010@gmail.com last updated on 27/Jul/20 $$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{1}×\mathrm{3}×\mathrm{5}}+\frac{\mathrm{3}}{\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}}+………\mathrm{n}−\mathrm{terms} \\ $$$$\mathrm{Find}\:\mathrm{sum} \\ $$ Answered by nimnim last updated on 27/Jul/20 $${Let}\:{S}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}×\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{1}×\mathrm{3}×\mathrm{5}}+\frac{\mathrm{3}}{\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}}+….{to}\:{n}\:{terms} \\ $$$${Nr}={n}^{{th}}…

lim-x-0-cosx-1-x-2-

Question Number 105246 by moonanddolldoll last updated on 27/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}{x}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \\ $$ Answered by bemath last updated on 27/Jul/20 $${another}\:{method} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\left(\mathrm{cos}\:{x}−\mathrm{1}\right)\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}}…

Solve-x-y-3-i-x-y-5-ii-

Question Number 170754 by Tawa11 last updated on 30/May/22 $$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\mathrm{x}\:\:\:\:+\:\:\:\sqrt{\mathrm{y}}\:\:\:\:=\:\:\:\:\mathrm{3}\:\:\:\:\:\:\:\:……\:\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\sqrt{\mathrm{x}}\:\:\:\:+\:\:\:\:\mathrm{y}\:\:\:\:=\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\:……\:\:\left(\mathrm{ii}\right) \\ $$ Commented by MJS_new last updated on 30/May/22 $$\mathrm{obviously}\:{x}=\mathrm{1}\wedge{y}=\mathrm{4} \\…