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((♣JS♥)/(•≡•)) (1) lim_(x→0) ((sin (tan x)−tan (sin x))/(x−sin x )) (2)lim_(x→∞) x^2 (√((1−cos ((2/x)))(√((1−cos ((2/x)))(√((1−cos ((2/x)))(√(...)))))))) ?

$$\:\:\:\:\:\:\frac{\clubsuit{JS}\heartsuit}{\bullet\equiv\bullet} \\ $$$$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{tan}\:\left(\mathrm{sin}\:{x}\right)}{{x}−\mathrm{sin}\:{x}\:} \\ $$$$\:\left(\mathrm{2}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{...}}}}\:?\: \\ $$$$ \\ $$

Question Number 107974 Answers: 1 Comments: 0

Σ_(k=1) ^n (√(1+(1/k^2 )+(1/((1+k)^2 ))))

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{k}\right)^{\mathrm{2}} }} \\ $$

Question Number 107871 Answers: 1 Comments: 1

((✓JS✓)/♥) lim_(x→0) (√((x tan x)/(sin 2x−cos 2x +1))) ?

$$\:\:\:\:\:\:\:\frac{\checkmark\mathcal{JS}\checkmark}{\heartsuit} \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\frac{{x}\:\mathrm{tan}\:{x}}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{1}}}\:?\: \\ $$

Question Number 107965 Answers: 2 Comments: 0

((⊚BeMath⊚)/) ∫ x (√(x/(2a−x))) dx ?

$$\:\:\:\:\frac{\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{} \\ $$$$\int\:{x}\:\sqrt{\frac{{x}}{\mathrm{2}{a}−{x}}}\:{dx}\:?\: \\ $$

Question Number 107947 Answers: 1 Comments: 0

Question Number 107946 Answers: 0 Comments: 0

Let a sequence {a_n } satisfies a_n = { ((2, n=1)),((2ln(a_(n−1) )+(1/a_(n−1) ) , n≥2)) :} Prove that a_n ≥1+(1/n) for all n∈N.

$$\mathrm{Let}\:\mathrm{a}\:\mathrm{sequence}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{satisfies} \\ $$$${a}_{\mathrm{n}} =\begin{cases}{\mathrm{2},\:\mathrm{n}=\mathrm{1}}\\{\mathrm{2ln}\left({a}_{\mathrm{n}−\mathrm{1}} \right)+\frac{\mathrm{1}}{{a}_{\mathrm{n}−\mathrm{1}} }\:,\:\mathrm{n}\geqslant\mathrm{2}}\end{cases} \\ $$$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$${a}_{\mathrm{n}} \geqslant\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\in\mathbb{N}. \\ $$

Question Number 107945 Answers: 3 Comments: 0

((○BeMath○)/(∧⌣∧)) { ((x^4 +(1/x^4 ) = 23)),((x^3 −(1/x^3 ) = ?)) :}

$$\:\:\:\:\:\:\frac{\circ\mathbb{B}{e}\mathbb{M}{ath}\circ}{\wedge\smile\wedge} \\ $$$$\:\:\:\begin{cases}{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:=\:\mathrm{23}}\\{{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:=\:?}\end{cases} \\ $$

Question Number 107941 Answers: 0 Comments: 1

Question Number 107932 Answers: 1 Comments: 3

((BeMath)/•) Given { ((tan (x−y)=(3/4))),((tan x = 2 )) :} find tan y ?

$$\:\:\:\frac{\mathbb{B}{e}\mathbb{M}{ath}}{\bullet} \\ $$$${Given}\:\begin{cases}{\mathrm{tan}\:\left({x}−{y}\right)=\frac{\mathrm{3}}{\mathrm{4}}}\\{\mathrm{tan}\:{x}\:=\:\mathrm{2}\:}\end{cases} \\ $$$${find}\:\:\mathrm{tan}\:{y}\:? \\ $$

Question Number 107930 Answers: 3 Comments: 0

((BeMath)/(•∩•)) lim_(x→0) (sin x)^(1/(ln (√x))) ?

$$\:\:\frac{\mathbb{B}{e}\mathbb{M}{ath}}{\bullet\cap\bullet} \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{ln}\:\sqrt{{x}}}} \:? \\ $$

Question Number 107929 Answers: 0 Comments: 0

(1/(1+2^2 +3^3 ))+(1/(2^2 +3^3 +4^4 ))+(1/(3^3 +4^4 +5^5 ))+....

$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} +\mathrm{4}^{\mathrm{4}} +\mathrm{5}^{\mathrm{5}} }+.... \\ $$

Question Number 107928 Answers: 0 Comments: 0

Question Number 107927 Answers: 0 Comments: 0

Question Number 107926 Answers: 2 Comments: 0

Question Number 107925 Answers: 2 Comments: 0

Question Number 107924 Answers: 1 Comments: 0

Question Number 107923 Answers: 3 Comments: 0

((⊚BeMath⊚)/) ∫_0 ^1 x^(9/2) (1−x)^(5/2) dx ?

$$\:\:\:\:\:\frac{\circledcirc\mathbb{B}{e}\mathcal{M}{ath}\circledcirc}{} \\ $$$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{\frac{\mathrm{9}}{\mathrm{2}}} \:\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:{dx}\:? \\ $$

Question Number 107922 Answers: 1 Comments: 0

if: y=(x/(x^2 +1)) then find (d(√y)/d(√x)) ?

$${if}:\:{y}=\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{then}\:{find}\:\frac{{d}\sqrt{{y}}}{{d}\sqrt{{x}}}\:? \\ $$

Question Number 107913 Answers: 0 Comments: 0

X_0 = ((X_1 .F_(y1) + X_2 .F_(y2) + .....)/(F_(y2) + F_(y2 ) + .....)) Y_0 = ((Y_1 .F_(x1) + Y_2 .F_(x2) + ......)/(F_(x1) + F_(x2) + ......)) X_0 = ((x_1 .m_1 + x_2 .m_2 + x_3 .m_3 + ....)/(m_1 + m_2 + m_3 + ......)) Y_0 = ((y_1 .m_1 + y_2 .m_2 + y_3 .m_3 + ....)/(m_1 + m_2 + m_3 + .....)) X_z = ((l_1 .x_1 + l_2 .x_2 + l_3 .x_3 + .......)/(l_1 + l_2 + l_3 + ......)) Y_z = ((l_1 .y_1 + l_2 .y_2 + l_3 .y_3 + ...... )/(l_1 + l_2 + l_3 + ......))

Question Number 107905 Answers: 1 Comments: 3

Which of the following set of horizontal forces would lead an object in equilibrium? (a) 5N 10N 20N (b) 6N 12N 18N (c) 8N 8N 8N (b) 2N 4N 8N 16N

$$\mathrm{W}{hich}\:{of}\:{the}\:{following}\:{set}\:{of}\:{horizontal} \\ $$$${forces}\:{would}\:{lead}\:{an}\:{object}\:{in}\:{equilibrium}? \\ $$$$\left({a}\right)\:\mathrm{5}{N}\:\:\:\mathrm{10}{N}\:\:\mathrm{20}{N} \\ $$$$\left({b}\right)\:\mathrm{6}{N}\:\:\:\mathrm{12}{N}\:\:\:\:\mathrm{18}{N} \\ $$$$\left({c}\right)\:\mathrm{8}{N}\:\:\:\mathrm{8}{N}\:\:\:\mathrm{8}{N} \\ $$$$\left({b}\right)\:\mathrm{2}{N}\:\:\:\:\mathrm{4}{N}\:\:\:\mathrm{8}{N}\:\:\:\mathrm{16}{N} \\ $$

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