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Category: Relation and Functions

hi-everybody-1-calculate-I-6-3-ln-tan-x-dx-2-calculate-lim-x-e-x-1-ln-x-x-e-

Question Number 144109 by henderson last updated on 21/Jun/21 $$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{everybody}}\:! \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{calculate}}\::\:\boldsymbol{\mathrm{I}}\:=\int_{\frac{\boldsymbol{\pi}}{\mathrm{6}}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{3}}} \boldsymbol{{ln}}\left(\boldsymbol{{tan}}\:\boldsymbol{{x}}\right)\boldsymbol{{dx}}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{calculate}}\:\::\:\underset{\boldsymbol{{x}}\:\rightarrow\:\boldsymbol{{e}}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{x}}\sqrt{\mathrm{1}−\boldsymbol{{ln}}\:\boldsymbol{{x}}}}{\boldsymbol{{x}}−\boldsymbol{{e}}}\:. \\ $$ Commented by bobhans last updated on…

f-f-x-f-x-2-

Question Number 391 by 123456 last updated on 25/Jan/15 $${f}\left[{f}\left({x}\right)\right]={f}\left({x}^{\mathrm{2}} \right) \\ $$ Answered by prakash jain last updated on 27/Dec/14 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{above}\:\mathrm{implies} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \\…

let-p-prime-not-0-and-n-integr-1-n-lt-p-prove-that-p-1-p-2-p-n-n-1-n-is-integr-and-divided-by-p-

Question Number 65915 by mathmax by abdo last updated on 05/Aug/19 $${let}\:{p}\:{prime}\:{not}\:\mathrm{0}\:\:{and}\:{n}\:{integr}\:/\mathrm{1}\leqslant{n}<{p}\:{prove}\:{that} \\ $$$$\frac{\left({p}−\mathrm{1}\right)\left({p}−\mathrm{2}\right)….\left({p}−{n}\right)}{{n}!}\:−\left(−\mathrm{1}\right)^{{n}} \:\:{is}\:{integr}\:{and}\:{divided}\:{by}\:{p} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

f-n-x-1-c-0-n-x-c-1-n-x-2-c-2-n-x-3-c-n-x-x-x-1-x-2-x-n-n-N-f-4-1-f-3-1-

Question Number 359 by 123456 last updated on 25/Jan/15 $${f}_{{n}} \left({x}\right)=\mathrm{1}+{c}_{\mathrm{0}} \left({n}\right){x}+{c}_{\mathrm{1}} \left({n}\right){x}^{\mathrm{2}} +{c}_{\mathrm{2}} \left({n}\right){x}^{\mathrm{3}} \\ $$$${c}_{{n}} \left({x}\right)={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}−{n}\right) \\ $$$${n}\in\mathbb{N} \\ $$$$\mid{f}_{\mathrm{4}} \left(\mathrm{1}\right)−{f}_{\mathrm{3}} \left(\mathrm{1}\right)\mid=? \\…