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Given-the-function-f-x-where-f-x-x-2-1-for-x-x-D-f-2-x-3-1-for-y-f-x-a-Evaluate-f-2-if-f-a-2-a-n-1-find-the-value-of-a-hence-the-domain-of-f-x-

Question Number 38535 by Rio Mike last updated on 27/Jun/18 $${Given}\:{the}\:{function} \\ $$$${f}\left({x}\right)\:{where}\: \\ $$$$ \\ $$$${f}\left({x}\right)=\:\begin{cases}{\int{x}^{\mathrm{2}} \:+\:\mathrm{1}\:,{for}\:\left\{{x}:{x}\:{D}\left({f}\right)\:\mathrm{2}\right.}\\{\int{x}^{\mathrm{3}} \:−\:\mathrm{1},{for}\:{y}\:=\:{f}'\left({x}\right)}\end{cases} \\ $$$$\left.{a}\right)\:{Evaluate}\:{f}\left(\mathrm{2}\right) \\ $$$${if}\:{f}\left({a}\right)=\:\mathrm{2}\:+\:{a}^{{n}−\mathrm{1}} \\ $$$${find}\:{the}\:{value}\:{of}\:{a}…

simlify-A-1-2-5-4-1-2-5-4-B-1-3-2-6-1-3-2-6-

Question Number 38517 by math khazana by abdo last updated on 26/Jun/18 $${simlify} \\ $$$${A}=\:\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{5}}\right)^{\mathrm{4}} }\:+\:\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{5}}\right)^{\mathrm{4}} } \\ $$$${B}\:=\:\frac{\mathrm{1}}{\left(\mathrm{3}−\sqrt{\mathrm{2}}\right)^{\mathrm{6}} }\:+\frac{\mathrm{1}}{\left(\mathrm{3}+\sqrt{\mathrm{2}}\right)^{\mathrm{6}} } \\ $$ Answered by…

prove-that-tan-3a-tan-2a-tan-a-tan-3a-tan-2a-tan-a-

Question Number 38495 by kunal1234523 last updated on 26/Jun/18 $${prove}\:{that} \\ $$$$\boldsymbol{\mathrm{tan}}\:\mathrm{3}\boldsymbol{{a}}\:\boldsymbol{\mathrm{tan}}\:\mathrm{2}\boldsymbol{{a}}\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{{a}}\:=\:\:\boldsymbol{\mathrm{tan}}\:\mathrm{3}\boldsymbol{{a}}\:−\:\boldsymbol{\mathrm{tan}}\:\mathrm{2}\boldsymbol{{a}}\:−\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{{a}} \\ $$ Answered by kunal1234523 last updated on 26/Jun/18 $${tan}\:\mathrm{3}{a}\:=\:{tan}\:\left({a}+\mathrm{2}{a}\right) \\ $$$$\Rightarrow{tan}\:\mathrm{3}{a}\:=\:\frac{{tan}\:{a}\:+\:{tan}\:\mathrm{2}{a}}{\mathrm{1}\:−\:{tan}\:{a}\:{tan}\:\mathrm{2}{a}} \\…

In-the-figure-below-a-particle-A-of-mass-2kg-is-lying-on-a-rough-wooden-block-The-particle-A-is-connected-by-a-light-inextensible-horizontal-string-passing-over-a-smooth-light-fixed-pulley-at-the-edge

Question Number 38420 by Rio Mike last updated on 25/Jun/18 $${In}\:{the}\:{figure}\:{below},{a}\:{particle}\:{A}\:{of} \\ $$$${mass}\:\mathrm{2}{kg}\:{is}\:{lying}\:{on}\:{a}\:{rough}\:{wooden} \\ $$$${block}.{The}\:{particle}\:{A}\:{is}\:{connected}\:{by} \\ $$$${a}\:{light}\:{inextensible}\:{horizontal}\:{string} \\ $$$${passing}\:{over}\:{a}\:{smooth}\:{light}\:{fixed} \\ $$$${pulley}\:{at}\:{the}\:{edge}\:{of}\:{the}\:{block},{to}\:{a} \\ $$$${particle}\:{B}\:{of}\:{mass}\:\mathrm{3}{kg}\:{which}\:{hangs} \\ $$$${freely}.\:{The}\:{coefficent}\:{of}\:{friction}…