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Author: Tinku Tara

Find-lim-n-n-p-x-n-where-p-Z-

Question Number 8633 by Yozzias last updated on 19/Oct/16 $$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{n}^{\mathrm{p}} }{\mathrm{x}^{\mathrm{n}} }\:\:\:\mathrm{where}\:\mathrm{p}\in\mathbb{Z}^{+} . \\ $$ Commented by prakash jain last updated on 19/Oct/16 $$\mathrm{Does}\:{x}\:\mathrm{cover}\:\mathrm{entire}\:\mathrm{range}\:\mathrm{of}\:\mathbb{R}?…

If-z-1-z-2-and-z-3-are-distinct-complex-numbers-such-that-z-1-z-2-z-3-1-and-z-1-2-z-2-z-3-z-2-2-z-3-z-1-z-3-2-z-1-z-2-1-then-the-value-o

Question Number 139700 by EnterUsername last updated on 30/Apr/21 $$\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{z}_{\mathrm{1}} ^{\mathrm{2}} }{{z}_{\mathrm{2}} {z}_{\mathrm{3}} }+\frac{{z}_{\mathrm{2}} ^{\mathrm{2}}…

is-it-always-satisfying-A-lim-n-f-n-x-dx-B-lim-n-f-n-x-dx-A-B-please-show-counter-example-checking-1-f-n-x-x-n-x-0-1-A-lim-n-0-1-x-n-dx-lim-n-1-n-1-x-n-1-0-B-0-1-

Question Number 8628 by sou1618 last updated on 18/Oct/16 $${is}\:{it}\:{always}\:{satisfying}? \\ $$$$\boldsymbol{{A}}=\mathrm{lim}\left[{n}\rightarrow\infty\right]\int{f}\left({n},{x}\right){dx} \\ $$$$\boldsymbol{{B}}=\int\mathrm{lim}\left[{n}\rightarrow\infty\right]{f}\left({n},{x}\right){dx} \\ $$$${A}={B}?? \\ $$$${please}\:{show}\:{counter}\:{example} \\ $$$$ \\ $$$$ \\ $$$${checking} \\…

In-an-entrance-examination-each-question-has-four-possible-answers-A-candidate-answers-three-question-by-guessing-a-find-the-probability-that-all-three-questions-are-wrong-b-find-the-probabili

Question Number 139697 by otchereabdullai@gmail.com last updated on 30/Apr/21 $$\mathrm{In}\:\mathrm{an}\:\mathrm{entrance}\:\mathrm{examination}\:\mathrm{each}\: \\ $$$$\mathrm{question}\:\mathrm{has}\:\mathrm{four}\:\mathrm{possible}\:\mathrm{answers}. \\ $$$$\mathrm{A}\:\mathrm{candidate}\:\mathrm{answers}\:\mathrm{three}\:\mathrm{question} \\ $$$$\mathrm{by}\:\mathrm{guessing}\:. \\ $$$$\mathrm{a}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{all}\:\mathrm{three}\: \\ $$$$\mathrm{questions}\:\mathrm{are}\:\mathrm{wrong}. \\ $$$$\mathrm{b}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{all}\:\mathrm{the}\: \\ $$$$\mathrm{questions}\:\mathrm{are}\:\mathrm{correct}. \\…