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the-hcf-of-two-numbers-is-75-and-their-lcm-is-3375-if-one-of-the-numbers-is-675-find-the-other-number-

Question Number 21253 by gopikrishnan005@gmail.com last updated on 17/Sep/17 $${the}\:{hcf}\:{of}\:{two}\:{numbers}\:{is}\:\mathrm{75}\:{and}\:{their}\:{lcm}\:{is}\:\mathrm{3375}\:{if}\:{one}\:{of}\:{the}\:{numbers}\:{is}\:\mathrm{675}\:{find}\:{the}\:{other}\:{number} \\ $$ Answered by Tinkutara last updated on 17/Sep/17 $$\mathrm{Product}\:\mathrm{of}\:\mathrm{two}\:\mathrm{numbers}\:=\:\mathrm{HCF}×\mathrm{LCM} \\ $$$$\mathrm{675}×{x}=\mathrm{75}×\mathrm{3375} \\ $$$${x}=\mathrm{375} \\…

show-that-lim-x-0-ln-1-x-x-1-x-1-2-

Question Number 152247 by mathocean1 last updated on 26/Aug/21 $${show}\:{that}\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}\:−\mathrm{1}}{{x}}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mr W last updated on 26/Aug/21 $$\mathrm{ln}\:\left(\mathrm{1}+{x}\right)={x}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{{x}^{\mathrm{4}} }{\mathrm{4}}+……

Question-152241

Question Number 152241 by ZiYangLee last updated on 26/Aug/21 Answered by Olaf_Thorendsen last updated on 26/Aug/21 $$\left({i}\right)\:\mathrm{and}\:\left({ii}\right)\:: \\ $$$${p}\left({x}\right)\:=\:{a}\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +{px}+{q}\right),\:{a}\neq\mathrm{0} \\ $$$$\left({iii}\right)\:: \\ $$$${p}\left(\mathrm{0}\right)\:=\:\mathrm{4}\:\Leftrightarrow\:−{aq}\:=\:\mathrm{4}\:\Rightarrow\:{q}\:=\:−\frac{\mathrm{4}}{{a}} \\…

1-for-x-gt-0-find-the-value-of-m-to-1-log-5-x-2-1-log-5-mx-2-4x-m-verify-x-

Question Number 152208 by SOMEDAVONG last updated on 26/Aug/21 $$\mathrm{1}.\mathrm{for}\:\forall\mathrm{x}>\mathrm{0}.\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{m}\:\mathrm{to}\: \\ $$$$\mathrm{1}+\mathrm{log}_{\mathrm{5}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\geqslant\mathrm{log}_{\mathrm{5}} \left(\mathrm{mx}^{\mathrm{2}} +\mathrm{4x}+\mathrm{m}\right)\:\mathrm{verify}\:\forall\mathrm{x}. \\ $$ Answered by Rasheed.Sindhi last updated on 26/Aug/21…