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Author: Tinku Tara

0-lt-c-lt-1-such-that-the-recursive-sequence-a-n-defined-by-setting-a-1-c-2-a-n-1-1-2-c-a-n-2-for-n-N-monotonic-and-convergent-

Question Number 213548 by universe last updated on 08/Nov/24 $$\mathrm{0}<{c}<\mathrm{1}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{recursive}\:\mathrm{sequence} \\ $$$$\left\{{a}_{{n}} \right\}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{setting}\: \\ $$$$\:\mathrm{a}_{\mathrm{1}\:} =\:\frac{\mathrm{c}}{\mathrm{2}}\:\:,\:{a}_{\mathrm{n}+\mathrm{1}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{c}+\mathrm{a}_{\mathrm{n}} ^{\mathrm{2}} \right)\:\:\mathrm{for}\:\mathrm{n}\in\:\mathbb{N} \\ $$$$\mathrm{monotonic}\:\mathrm{and}\:\mathrm{convergent} \\ $$ Answered by…

f-z-j-z-z-2-j-2-z-0-lim-z-f-z-

Question Number 213555 by issac last updated on 08/Nov/24 $${f}\left({z}\right)=\underset{{j}=−\infty} {\overset{\infty} {\sum}}\:\frac{{z}}{{z}^{\mathrm{2}} +{j}^{\mathrm{2}} }\:,\:{z}\in\left(\mathrm{0},\infty\right) \\ $$$$\underset{{z}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({z}\right)=?? \\ $$ Answered by lepuissantcedricjunior last updated on…

Are-not-there-simple-means-of-solving-this-system-of-equations-in-non-negative-reals-

Question Number 213535 by justenspi last updated on 07/Nov/24 $$\mathrm{Are}\:\mathrm{not}\:\mathrm{there}\:\mathrm{simple}\:\mathrm{means}\:\mathrm{of}\:\mathrm{solving}\:\mathrm{this} \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\:\mathrm{in}\:\mathrm{non}-\mathrm{negative}\:\mathrm{reals} \\ $$ Commented by justenspi last updated on 07/Nov/24 Terms of Service Privacy…

The-two-corner-points-of-a-square-lie-on-curve-f-x-x-2-2x-3-and-the-other-two-corner-points-lie-on-curve-g-x-x-2-2x-3-It-is-known-that-the-area-of-a-square-can-be-expressed-by-p-

Question Number 213522 by efronzo1 last updated on 07/Nov/24 $$\:\:\mathrm{The}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\: \\ $$$$\:\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}\:\mathrm{and}\: \\ $$$$\:\mathrm{the}\:\mathrm{other}\:\mathrm{two}\:\mathrm{corner}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\: \\ $$$$\:\mathrm{curve}\:\mathrm{g}\left(\mathrm{x}\right)=\:−\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{3}\:.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known} \\ $$$$\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\:\:\mathrm{expressed}\:\mathrm{by}\:\mathrm{p}+\mathrm{q}\sqrt{\mathrm{r}}\:,\:\mathrm{for}\:\mathrm{a}\:\mathrm{natural}\: \\ $$$$\:\mathrm{number}\:\mathrm{p},\mathrm{q}\:,\mathrm{r}\:\mathrm{where}\:\mathrm{r}\:\mathrm{is}\:\mathrm{not}\:\mathrm{divisible}\: \\…

0-2pi-z-sin-z-1-cos-2-z-dz-z-2-1-z-2-1-dz-z-2-sin-z-z-2-1-dz-

Question Number 213518 by issac last updated on 07/Nov/24 $$\int_{\mathrm{0}} ^{\:\mathrm{2}\pi} \:\frac{{z}\centerdot\mathrm{sin}\left({z}\right)}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left({z}\right)}\:\mathrm{d}{z} \\ $$$$\int_{\:\mid{z}\mid=\mathrm{2}} \:\frac{\mathrm{1}}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$$$\int_{\:\mid{z}\mid=\mathrm{2}} \:\frac{\mathrm{sin}\left({z}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$ Answered by…