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Question Number 175579 Answers: 0 Comments: 0
$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{1}−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} .\left(\mathrm{x}^{\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} −\mathrm{1}\right)}{\mathrm{ln}\:\mathrm{x}} \\ $$
Question Number 175573 Answers: 0 Comments: 0
Question Number 175572 Answers: 0 Comments: 0
Question Number 175571 Answers: 2 Comments: 0
Question Number 175567 Answers: 0 Comments: 0
$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{put}\:\mathrm{40} \\ $$$${identical}\:{balls}\:{into}\:\mathrm{20}\:{identical}\:{boxes} \\ $$$${such}\:{that}\:{each}\:{box}\:{obtains}\:{at}\:{least}\:{one} \\ $$$${ball}\:{and}\:{at}\:{most}\:\mathrm{5}\:{balls}? \\ $$
Question Number 175568 Answers: 1 Comments: 1
Question Number 175554 Answers: 2 Comments: 0
$${x}^{\sqrt{{x}}} =\sqrt{{x}^{{x}} } \\ $$$${find}\:{x} \\ $$
Question Number 175553 Answers: 1 Comments: 0
Question Number 175548 Answers: 1 Comments: 4
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\begin{array}{|c|}{\overset{\underset{−} {\overline {\mid\bullet\mid}}} {\:\begin{array}{|c|}{\underset{} {\overset{} {\mathrm{2}+\mathrm{424}+\mathrm{44244}+\mathrm{4442444}+\centerdot\centerdot\centerdot{n}\:{terms}=?_{} ^{} }}}\\\hline\end{array}_{} ^{} }}\\\hline\end{array} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$
Question Number 175547 Answers: 2 Comments: 0
Question Number 175544 Answers: 1 Comments: 1
$$\:\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{10}°\right)+\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{50}°\right)+\mathrm{tan}\:^{\mathrm{6}} \left(\mathrm{70}°\right)=? \\ $$
Question Number 175531 Answers: 2 Comments: 0
$$\:\int\:\frac{{dt}}{\mathrm{5cos}\:{t}+\mathrm{6sin}\:{t}}\:=? \\ $$
Question Number 175511 Answers: 0 Comments: 1
Question Number 175516 Answers: 1 Comments: 0
Question Number 175505 Answers: 1 Comments: 2
$${N}=\mathrm{64990691606209}\:\mathrm{is}\:\mathrm{a}\:\mathrm{semi}-\mathrm{prime}\:\mathrm{number}. \\ $$$$\mathrm{That}\:\mathrm{is},\:{N}={pq}\:\mathrm{where}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{prime}\:\mathrm{numbers}. \\ $$$$\mathrm{Find}\:{p}\:\mathrm{and}\:{q}: \\ $$
Question Number 175493 Answers: 1 Comments: 1
$$\mathrm{tan}^{−\mathrm{1}} \left({a}\mathrm{sin}\:\theta\right)=\mathrm{sin}^{−\mathrm{1}} {b}−\theta \\ $$$${find}\:\theta. \\ $$
Question Number 175490 Answers: 1 Comments: 0
$${solve} \\ $$$${f}\left({x}\right){f}\left({y}\right)=\:{f}\left({x}+{y}\right)+{xy} \\ $$$${f}:\mathbb{R}\Rightarrow\mathbb{R} \\ $$
Question Number 175487 Answers: 0 Comments: 0
Question Number 175483 Answers: 2 Comments: 0
$${Solve}\:{it}\:{by}\:{horner}'{s}\:{method}\:{and}\:{get} \\ $$$${the}\:{quotient}. \\ $$$$\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right)=? \\ $$
Question Number 175476 Answers: 1 Comments: 1
Question Number 175471 Answers: 1 Comments: 0
Question Number 175470 Answers: 1 Comments: 0
Question Number 175467 Answers: 0 Comments: 1
Question Number 175466 Answers: 0 Comments: 0
Question Number 175464 Answers: 2 Comments: 0
$$\:\mathrm{Find}\:\mathrm{general}\:\mathrm{solutions}\:\mathrm{the}\:\mathrm{following}\: \\ $$$$\mathrm{differential}\:\mathrm{equations} \\ $$$$\left({a}\right)\:\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:=\:\mathrm{6}{y} \\ $$$$\left(\mathrm{b}\right)\:\:\:\left(\mathrm{3}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dx}\:+\:\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dy}\:=\:\mathrm{0} \\ $$$$ \\ $$
Question Number 175462 Answers: 1 Comments: 3
$${p}^{\mathrm{3}} +{q}^{\mathrm{3}} +{p}^{\mathrm{2}} +{q}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:{p}+{q}\:{in}\:{terms}\:{of}\:{c}.\:\:{if}\:\:{c}^{\mathrm{2}} <\frac{\mathrm{4}}{\mathrm{9}}. \\ $$
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