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Category: Relation and Functions

Prove-that-n-1-2-n-2-4-n-4-8-n-8-16-n-Such-that-denotes-greatest-integer-function-and-n-N-

Question Number 7317 by lakshaysethi last updated on 24/Aug/16 $${Prove}\:{that}\:\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]+\left[\frac{{n}+\mathrm{2}}{\mathrm{4}}\right]+\left[\frac{{n}+\mathrm{4}}{\mathrm{8}}\right]+\left[\frac{{n}+\mathrm{8}}{\:\mathrm{16}}\right]+……..={n}. \\ $$$${Such}\:{that}\:\left[.\right]\:{denotes}\:{greatest}\:{integer}\:{function}\:{and}\:{n}\in{N}. \\ $$ Commented by FilupSmith last updated on 23/Aug/16 $${S}=\underset{{t}=\mathrm{1}} {\overset{\infty} {\sum}}\lceil\frac{{n}+\mathrm{2}^{{t}−\mathrm{1}} }{\mathrm{2}^{{t}}…

the-bottom-1-2-of-log-1-2-x-wants-to-make-2-2-how-

Question Number 6877 by sarathon last updated on 01/Aug/16 $$\mathrm{the}\:\mathrm{bottom}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\mathrm{of}\:\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} {x}\:\:\mathrm{wants}\:\mathrm{to}\:\mathrm{make}\:\:\mathrm{2} \\ $$$$\mathrm{2}\:\:\mathrm{how}?? \\ $$$$ \\ $$ Commented by Tawakalitu. last updated on 01/Aug/16 $${log}_{\frac{\mathrm{1}}{\mathrm{2}}}…

let-f-x-cos-narccosx-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-

Question Number 72393 by mathmax by abdo last updated on 28/Oct/19 $${let}\:{f}\left({x}\right)\:={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Terms of Service Privacy Policy…

Let-f-x-x-2-2x-3-x-1-amp-g-x-1-x-4-x-4-then-the-number-of-real-solutions-of-equation-f-x-g-x-is-

Question Number 137817 by bramlexs22 last updated on 07/Apr/21 $${Let}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3};\:{x}\geqslant\mathrm{1}\:\& \\ $$$${g}\left({x}\right)=\mathrm{1}+\sqrt{{x}+\mathrm{4}}\:;\:{x}\geqslant−\mathrm{4}\:{then} \\ $$$${the}\:{number}\:{of}\:{real}\:{solutions} \\ $$$${of}\:{equation}\:{f}\left({x}\right)={g}\left({x}\right)\:{is}\:… \\ $$ Answered by MJS_new last updated on…

let-f-x-2x-3-x-2-1-calculate-f-n-x-2-find-f-10-x-and-f-15-x-3-calculate-f-10-0-and-f-15-0-4-developp-f-at-integr-serie-5-let-g-x-0-x-f-t-dt-developp-g-at-in

Question Number 72260 by mathmax by abdo last updated on 26/Oct/19 $${let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${calculate}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{f}^{\left(\mathrm{10}\right)} \left({x}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left({x}\right) \\ $$$$\left.\mathrm{3}\right){calculate}\:{f}^{\left(\mathrm{10}\right)} \left(\mathrm{0}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left(\mathrm{0}\right) \\…