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Question Number 31899 Answers: 1 Comments: 0
Question Number 31898 Answers: 0 Comments: 0
Question Number 31895 Answers: 0 Comments: 3
Question Number 31894 Answers: 0 Comments: 9
Question Number 31919 Answers: 1 Comments: 3
Question Number 32372 Answers: 1 Comments: 0
Question Number 31868 Answers: 0 Comments: 0
$${Let}\:{a}>{b}>\mathrm{1}\:{be}\:{positive}\:{integers}\:{with}\:{b}\:{odd}. \\ $$$${Let}\:{n}\:{be}\:{a}\:{positive}\:{integer}\:{as}\:{well}.\:{If}\:\:{b}^{{n}} \:{divides} \\ $$$${a}^{{n}} −\mathrm{1},\:{prove}\:{that}\:{a}^{{b}} \:>\:\frac{\mathrm{3}^{{n}} }{{n}}. \\ $$$${Solution}\:{please}.\:{Thanks}\:{in}\:{advance}!! \\ $$
Question Number 31865 Answers: 1 Comments: 6
$${Range}\:{of}\:{function}\:: \\ $$$${f}\left({x}\right)=\:\mathrm{6}^{{x}} +\mathrm{3}^{{x}} +\mathrm{6}^{−{x}} +\mathrm{3}^{−{x}} +\mathrm{2}. \\ $$
Question Number 31864 Answers: 1 Comments: 0
$${Let}\:{S}_{{n}} =\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\left(−\mathrm{1}\right)^{\frac{{k}\left({k}+\mathrm{1}\right)}{\mathrm{2}}} {k}^{\mathrm{2}} . \\ $$$${Then}\:{S}_{{n}} \:{can}\:{take}\:{the}\:{value}\left({s}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{1056} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1088} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{1120} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{1332}. \\ $$
Question Number 31863 Answers: 0 Comments: 9
Question Number 31858 Answers: 0 Comments: 1
$$\int\frac{{sinx}}{{x}}{dx} \\ $$
Question Number 31846 Answers: 1 Comments: 2
$$\mathrm{25}\left[\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} \right]=\left(\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}\right)^{\mathrm{2}} \\ $$$${is}\:{the}\:{equation}\:{of}\:{parabola}.{Find} \\ $$$${length}\:{of}\:{latus}\:{rectum} \\ $$
Question Number 31839 Answers: 0 Comments: 1
$${I}\:=\:\int\:\sqrt{{x}\:+\:\sqrt{{x}^{\mathrm{2}} \:−\:\mathrm{1}}}\:{dx} \\ $$
Question Number 31838 Answers: 0 Comments: 0
$$\mathrm{Given} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{3}}{\mathrm{16}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}\right){x}^{\mathrm{2}} \:−\:\frac{\mathrm{9}}{\mathrm{10}}\left(\int_{\mathrm{0}} ^{\mathrm{2}} \:{f}\left({x}\right){dx}\right){x}\:+\:\mathrm{2}\left(\int_{\mathrm{0}} ^{\mathrm{3}} \:{f}\left({x}\right){dx}\right)\:+\:\mathrm{4} \\ $$$$\mathrm{Solve} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{t}\:+\:\left(\int_{{f}\left(\mathrm{2}\right)\:+\:\mathrm{2}} ^{{f}^{−\mathrm{1}} \left({t}\right)} \left[{f}\:'\left({x}\right)\right]^{\mathrm{2}} \:{dx}\right)}{\mathrm{1}\:−\:\mathrm{cos}\:{t}\:\mathrm{cosh}\:\mathrm{2}{t}\:\mathrm{cos}\:\mathrm{3}{t}} \\ $$
Question Number 31835 Answers: 0 Comments: 5
Question Number 31833 Answers: 1 Comments: 0
Question Number 31822 Answers: 1 Comments: 0
Question Number 31820 Answers: 1 Comments: 0
Question Number 31812 Answers: 2 Comments: 0
$${Find}\:{the}\:{equation}\:{of}\:{the}\:{line} \\ $$$${that}\:{is}\:{tangent}\:{to}\:{the}\:{curve}\:{y}={x}^{\mathrm{3}} \\ $$$${and}\:{is}\:{parallel}\:{to}\:{the}\:{line} \\ $$$$\mathrm{3}{x}−{y}+\mathrm{1}=\mathrm{0} \\ $$
Question Number 31811 Answers: 1 Comments: 2
$${find}\:{the}\:{domain}\:{of} \\ $$$${f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{7}}{\left[\mathrm{2}−{x}^{\mathrm{2}} \right]} \\ $$
Question Number 31809 Answers: 0 Comments: 1
$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\frac{{x}−\mathrm{1}}{\left[{x}\right]} \\ $$
Question Number 31808 Answers: 0 Comments: 2
$$\mathrm{The}\:\mathrm{numeric}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{is}: \\ $$$$ \\ $$$$\frac{\mathrm{Sec}\:\mathrm{1320}°}{\mathrm{2}}\:−\:\mathrm{2}\:\centerdot\:\mathrm{cos}\:\left(\frac{\mathrm{53}\pi}{\mathrm{3}}\right)\:+\:\left(\mathrm{tg}\:\mathrm{2220}°\right)^{\mathrm{2}} \\ $$
Question Number 31804 Answers: 1 Comments: 0
$${A}\:{quadratic}\:{equation}\:{p}\left({x}\right)=\mathrm{0}\:{having} \\ $$$${coefficient}\:{of}\:{x}^{\mathrm{2}} \:{unity}\:{is}\:{such}\:{that} \\ $$$${p}\left({x}\right)=\mathrm{0}\:{and}\:{p}\left({p}\left({p}\left({x}\right)\right)\right)=\mathrm{0}\:{have}\:{a}\: \\ $$$${common}\:{root}\:{then}, \\ $$$${prove}\:{that}\::\:\:{p}\left(\mathrm{0}\right)×{p}\left(\mathrm{1}\right)=\mathrm{0}. \\ $$
Question Number 31794 Answers: 0 Comments: 2
Question Number 31792 Answers: 0 Comments: 4
Question Number 31787 Answers: 2 Comments: 0
$$\int\frac{\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{8}}{dx} \\ $$
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