Question and Answers Forum
All Questions Topic List
OthersQuestion and Answers: Page 55
Question Number 107362 Answers: 0 Comments: 1
$$\int_{\mathrm{0}} ^{\infty} \mathrm{x}^{\pi} \mathrm{e}^{−\mathrm{x}} \mathrm{dx} \\ $$
Question Number 107353 Answers: 2 Comments: 0
$${If}\:\mathrm{a}\:\mathrm{b}\:\mathrm{13}\:\mathrm{c}\:\mathrm{d}\:\mathrm{25}\:\mathrm{are}\:\mathrm{six}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}{P}\:.{find}\:{tbe}\:{value}\:{of}\:{a}\:{b}\:{c}\:{and}\:{d}. \\ $$
Question Number 107264 Answers: 2 Comments: 1
$$\int_{\mathrm{0}} ^{\infty} \lfloor\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\rfloor\mathrm{dx} \\ $$
Question Number 107263 Answers: 0 Comments: 1
$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{n}} \\ $$
Question Number 107187 Answers: 1 Comments: 3
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\sqrt{\mathrm{8}}=\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{3}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}+\frac{\mathrm{3}.\mathrm{5}.\mathrm{7}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}+...... \\ $$
Question Number 107178 Answers: 1 Comments: 1
Question Number 107101 Answers: 0 Comments: 0
$$\mathrm{Fun}\:\mathrm{time} \\ $$$$ \\ $$$$\mathrm{1}+\mathrm{2x}+\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} +....=\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\mathrm{1}+\mathrm{4}+\mathrm{12}+\mathrm{32}+...=\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\mathrm{4}+\mathrm{12}+\mathrm{32}+....=\mathrm{0}\:\:\left(\mathrm{No}\:\mathrm{1}\:\mathrm{fun}\right) \\ $$$$ \\ $$$$\mathrm{5}+\mathrm{11}+\mathrm{17}+\mathrm{23}+...=\mathrm{0}\:\:\: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{6n}−\mathrm{1}=\mathrm{6}\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{n}−\overset{\infty} {\sum}\mathrm{1}=\mathrm{6}.\left(−\frac{\mathrm{1}}{\mathrm{12}}\right)−\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{0} \\ $$$$\overset{\infty} {\sum}\mathrm{n}=−\frac{\mathrm{1}}{\mathrm{12}}\:\:\:\:\left(\mathrm{Ramanujan}\:\mathrm{sum}\right) \\ $$$$\overset{\infty} {\sum}\mathrm{1}=\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+...=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\overset{\infty} {\sum}\mathrm{n}^{\mathrm{2}} .\overset{\infty} {\sum}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\geqslant\left(\overset{\infty} {\sum}\mathrm{1}\right)^{\mathrm{2}} \:\:\:\left(\mathrm{Cauchy}\:\mathrm{schwarz}\:\mathrm{ineqality}\right) \\ $$$$\overset{\infty} {\sum}\mathrm{n}^{\mathrm{2}} .\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\geqslant\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\overset{\infty} {\sum}\mathrm{n}^{\mathrm{2}} \geqslant\frac{\mathrm{3}}{\mathrm{2}\pi^{\mathrm{2}} } \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Question Number 107092 Answers: 1 Comments: 2
Question Number 106828 Answers: 0 Comments: 2
$$\:\int\:\frac{\mathrm{1}}{{xdx}}\:{is}\:{that}\:{true}! \\ $$
Question Number 106825 Answers: 5 Comments: 0
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sin}\mathrm{5}{x}\:−\:{tan}\mathrm{5}{x}}{{x}^{\mathrm{3}} } \\ $$
Question Number 106694 Answers: 3 Comments: 0
Question Number 106653 Answers: 0 Comments: 7
$$\mathrm{30}+\mathrm{144}+\mathrm{420}+\mathrm{960}+\mathrm{1890}+\mathrm{3360}+...{n} \\ $$
Question Number 106637 Answers: 1 Comments: 0
$$\:\:\:\:\:\:@\mathrm{JS}@ \\ $$$$\mathrm{The}\:\mathrm{quartic}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{14x}+\mathrm{15}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1}+\mathrm{2i}\:.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{three}\:\mathrm{roots}.\: \\ $$
Question Number 106630 Answers: 2 Comments: 0
$${Find}\:{n}\:{in}\:{this}\:{equation}: \\ $$$$\left(−\mathrm{2}\right)^{{n}} \:=\:\mathrm{4096} \\ $$
Question Number 106526 Answers: 0 Comments: 2
Question Number 106503 Answers: 0 Comments: 11
$$\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{18}}+\frac{\mathrm{2}}{\mathrm{27}}+\frac{\mathrm{2}}{\mathrm{324}}+.... \\ $$
Question Number 106454 Answers: 0 Comments: 0
Question Number 106432 Answers: 0 Comments: 5
Question Number 106382 Answers: 0 Comments: 0
Question Number 106373 Answers: 1 Comments: 0
$$ \\ $$$$\mathrm{A}\:\mathrm{ladder}\:\mathrm{placed}\:\mathrm{against}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{walls} \\ $$$$\mathrm{ubtends}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}\:\mathrm{degree}\:\mathrm{with}\: \\ $$$$\mathrm{thewall}\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{footo} \\ $$$$\mathrm{f}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{is}\:\mathrm{15mt} \\ $$$$\mathrm{calculae}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ladder}\: \\ $$$$\mathrm{correctto}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$
Question Number 106366 Answers: 1 Comments: 0
Question Number 106363 Answers: 0 Comments: 0
$${prove}\:{that}\:: \\ $$$$\lfloor\frac{\sqrt{\mathrm{10}^{\mathrm{2}{k}} −\mathrm{1}}}{\mathrm{3}}\rfloor\:=\:\frac{\mathrm{10}^{{k}} \:−\mathrm{1}}{\mathrm{3}} \\ $$$$ \\ $$
Question Number 106360 Answers: 0 Comments: 0
Question Number 106337 Answers: 3 Comments: 4
$$\mathrm{1}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{9}}{\mathrm{4}}+\frac{\mathrm{13}}{\mathrm{8}}+\frac{\mathrm{17}}{\mathrm{16}}+...... \\ $$
Question Number 106333 Answers: 0 Comments: 1
Question Number 106329 Answers: 2 Comments: 0
$${find}\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\right){dx}\:\:{whithout}\:{using} \\ $$$${trigonometric}\:{compensation} \\ $$
Pg 50 Pg 51 Pg 52 Pg 53 Pg 54 Pg 55 Pg 56 Pg 57 Pg 58 Pg 59
Terms of Service
Privacy Policy
Contact: info@tinkutara.com