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Question Number 111103 Answers: 3 Comments: 0
$$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{3x}\right)}{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{8x}\right)}\:? \\ $$$$\left[\:\mathrm{Without}\:\mathrm{L}'\mathrm{Hopital}\:\right] \\ $$$$ \\ $$
Question Number 111100 Answers: 2 Comments: 0
$$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:? \\ $$
Question Number 111069 Answers: 0 Comments: 0
$$\theta''\left({t}\right)+\frac{{g}}{{l}}{sin}\theta=\mathrm{0} \\ $$
Question Number 111067 Answers: 0 Comments: 2
Question Number 111062 Answers: 0 Comments: 2
Question Number 111048 Answers: 0 Comments: 0
Question Number 111047 Answers: 0 Comments: 0
Question Number 111046 Answers: 0 Comments: 1
Question Number 111045 Answers: 0 Comments: 0
Question Number 111044 Answers: 1 Comments: 4
Question Number 111043 Answers: 0 Comments: 0
$${solve}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\sqrt{{x}}\left(\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{4}}} }{dx} \\ $$
Question Number 111039 Answers: 1 Comments: 0
$${solve}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$$${mr}\:\:{abbo}\:{your}\:{question}\: \\ $$
Question Number 111035 Answers: 1 Comments: 0
$$\mathrm{If}\:{b}\in\mathbb{Z}^{+} \:\forall\:\mathrm{both}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} −{bx}+\mathrm{132}=\mathrm{0}\:\mathrm{are}\:\mathrm{integers}. \\ $$$$\mathrm{Find} \\ $$$$\left(\mathrm{1}\right)\mathrm{the}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b} \\ $$$$\left(\mathrm{2}\right)\mathrm{the}\:\mathrm{smallest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b}. \\ $$
Question Number 111029 Answers: 1 Comments: 0
Question Number 111083 Answers: 2 Comments: 0
$$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} \:−\mathrm{1}\right)\: \\ $$$$\left(\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{asymptotes}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:−\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1}\: \\ $$
Question Number 111082 Answers: 1 Comments: 1
$$\:\:\:\left[\int_{\mathrm{0}} ^{\infty} {JS}\:{dx}\:\right] \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sin}\:\left({x}\right)\left(\mathrm{4}+\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)}{\left(\mathrm{4}−\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)^{\mathrm{2}} }\:{dx}\:? \\ $$
Question Number 111080 Answers: 1 Comments: 0
$$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\underset{\mathrm{k}=\mathrm{50}} {\overset{\mathrm{100}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{151}−\mathrm{k}\right)}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{and}\:\mathrm{series}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{x}} \\ $$
Question Number 111079 Answers: 1 Comments: 0
Question Number 111027 Answers: 0 Comments: 0
$$\:\:\bigstar\frac{\mathrm{log}\:_{{JS}} \left({farmer}\right)}{}\bigstar \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{tan}\:\left(\mathrm{ln}\:{x}\right)\mathrm{tan}\:\left(\mathrm{ln}\:\left(\frac{{x}}{\mathrm{2}}\right)\right){dx}}{{x}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right)\:<\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:;\:{where} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$
Question Number 111025 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$
Question Number 111024 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{lnx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\mathrm{dx} \\ $$
Question Number 111023 Answers: 1 Comments: 1
$$\int\frac{{sin}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 111011 Answers: 1 Comments: 0
$${solve}:\:{y}^{''} +{y}^{'} ={tanx} \\ $$
Question Number 111010 Answers: 1 Comments: 0
$$\int{e}^{{x}} \:{tanx}\:{dx} \\ $$
Question Number 111008 Answers: 0 Comments: 3
$$\frac{\sqrt{\boldsymbol{{x}}+\mathrm{1}}}{\boldsymbol{{y}}+\mathrm{2}}\:+\:\frac{\sqrt{\boldsymbol{{y}}+\mathrm{2}}}{\boldsymbol{{x}}+\mathrm{1}}\:=\mathrm{1}\:\:\:\:\:\:=>\:\:\boldsymbol{{x}}=? \\ $$
Question Number 111006 Answers: 0 Comments: 2
$$\mathrm{The}\:\mathrm{vectors}\:\boldsymbol{\mathrm{p}},\boldsymbol{\mathrm{q}}\:\mathrm{and}\:\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{mutially}\:\mathrm{perpendicularwith} \\ $$$$\mid\boldsymbol{\mathrm{q}}\mid=\mathrm{3}\:\mathrm{and}\:\mid\boldsymbol{\mathrm{r}}\mid=\sqrt{\mathrm{5}.\mathrm{4}\:}\:.\mathrm{If}\:\mathrm{X}=\:\mathrm{7}\boldsymbol{\mathrm{p}}+\mathrm{5}\boldsymbol{\mathrm{q}}+\mathrm{7}\boldsymbol{\mathrm{r}}\:\mathrm{and} \\ $$$$\mathrm{Y}=\mathrm{2}\boldsymbol{\mathrm{p}}+\mathrm{3}\boldsymbol{\mathrm{q}}−\mathrm{5}\boldsymbol{\mathrm{r}}\:\mathrm{are}\:\mathrm{perpendicular},\:\mathrm{find}\mid\boldsymbol{\mathrm{p}}\mid. \\ $$
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