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AllQuestion and Answers: Page 629

Question Number 155461 Answers: 0 Comments: 0

Question Number 155450 Answers: 2 Comments: 0

Question Number 155438 Answers: 0 Comments: 0

Question Number 155436 Answers: 0 Comments: 0

S = Σ_(m=0) ^∞ (1/(Σ_(n=0) ^m 10^n + m))

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{S}\:=\:\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\underset{{n}=\mathrm{0}} {\overset{{m}} {\sum}}\:\mathrm{10}^{{n}} +\:{m}} \\ $$$$\: \\ $$

Question Number 155428 Answers: 2 Comments: 0

simplify t=(((26)/(3(√3)))+5)^(1/3) −(((26)/(3(√3)))−5)^(1/3)

$${simplify} \\ $$$${t}=\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}+\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} −\left(\frac{\mathrm{26}}{\mathrm{3}\sqrt{\mathrm{3}}}−\mathrm{5}\right)^{\mathrm{1}/\mathrm{3}} \\ $$

Question Number 155426 Answers: 1 Comments: 2

Question Number 155420 Answers: 1 Comments: 0

(1/(42))+(1/(72))+(1/(110))+…=?

$$\frac{\mathrm{1}}{\mathrm{42}}+\frac{\mathrm{1}}{\mathrm{72}}+\frac{\mathrm{1}}{\mathrm{110}}+\ldots=? \\ $$

Question Number 155400 Answers: 0 Comments: 1

x^2 +x+5xy+6y^2 +2y−2=0

$${x}^{\mathrm{2}} +{x}+\mathrm{5}{xy}+\mathrm{6}{y}^{\mathrm{2}} +\mathrm{2}{y}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 155399 Answers: 2 Comments: 0

Question Number 155393 Answers: 1 Comments: 0

∣∣x−4∣−4∣ ≥ 4

$$\:\:\mid\mid\mathrm{x}−\mathrm{4}\mid−\mathrm{4}\mid\:\geqslant\:\mathrm{4}\: \\ $$

Question Number 155392 Answers: 0 Comments: 0

lim_(x→0) ((((a^(x+1) +b^(x+1) )^2 )/(a+b)))^(1/x) =…?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\left({a}^{{x}+\mathrm{1}} +{b}^{{x}+\mathrm{1}} \right)^{\mathrm{2}} }{{a}+{b}}\right)^{\frac{\mathrm{1}}{{x}}} =\ldots? \\ $$

Question Number 155386 Answers: 1 Comments: 0

Prove that: Σ_(k=1) ^∞ (((H_k )^3 )/2^k ) = ((3ζ(3) + ln^3 2 + π^2 ln2)/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{H}_{\boldsymbol{\mathrm{k}}} \right)^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\:=\:\frac{\mathrm{3}\zeta\left(\mathrm{3}\right)\:+\:\mathrm{ln}^{\mathrm{3}} \mathrm{2}\:+\:\pi^{\mathrm{2}} \mathrm{ln2}}{\mathrm{3}}\:\: \\ $$

Question Number 155384 Answers: 2 Comments: 1

Solve : x^2 − (5−i)x + (12−5i) = 0

$$\boldsymbol{{Solve}}\::\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\left(\mathrm{5}−\boldsymbol{{i}}\right)\boldsymbol{{x}}\:+\:\left(\mathrm{12}−\mathrm{5}\boldsymbol{{i}}\right)\:=\:\mathrm{0} \\ $$

Question Number 156093 Answers: 2 Comments: 0

Question Number 155382 Answers: 1 Comments: 0

Question Number 155381 Answers: 1 Comments: 5

Question Number 155377 Answers: 2 Comments: 0

For two non-negative real numbers: a^6 + b^6 = 2 Find a;b such that 3(a+b)=1+5(√(ab))

$$\mathrm{For}\:\mathrm{two}\:\mathrm{non}-\mathrm{negative}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{a}^{\mathrm{6}} \:+\:\mathrm{b}^{\mathrm{6}} \:=\:\mathrm{2} \\ $$$$\mathrm{Find}\:\:\mathrm{a};\mathrm{b}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{3}\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{1}+\mathrm{5}\sqrt{\mathrm{ab}} \\ $$

Question Number 155372 Answers: 1 Comments: 4

Question Number 155365 Answers: 2 Comments: 0

y=((10)/((2x^2 +1)^5 )) find (dy/dx)

$$\:{y}=\frac{\mathrm{10}}{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{5}} } \\ $$$$\:{find}\:\:\frac{{dy}}{{dx}} \\ $$

Question Number 155362 Answers: 0 Comments: 0

if a;b≥0 and a^4 + b^4 = 17 prove that: 15(a + b) ≥ 17 + 14(√(2ab))

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{4}} \:+\:\mathrm{b}^{\mathrm{4}} \:=\:\mathrm{17}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{15}\left(\mathrm{a}\:+\:\mathrm{b}\right)\:\geqslant\:\mathrm{17}\:+\:\mathrm{14}\sqrt{\mathrm{2ab}} \\ $$$$ \\ $$

Question Number 155361 Answers: 0 Comments: 0

x−4z+8y=7 8×+7z−y=4 x^2 +y^2 −z^2 =?

$${x}−\mathrm{4}{z}+\mathrm{8}{y}=\mathrm{7} \\ $$$$\mathrm{8}×+\mathrm{7}{z}−{y}=\mathrm{4} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} =? \\ $$

Question Number 155360 Answers: 1 Comments: 0

Question Number 155359 Answers: 0 Comments: 1

Question Number 155357 Answers: 1 Comments: 1

Question Number 155356 Answers: 0 Comments: 0

Find the coefficient of term “ a^m b^(2m) ” in (1+a)^m (1+b)^(n+m) (1+a+b)^m .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{term}\:``\:\mathrm{a}^{\mathrm{m}} \mathrm{b}^{\mathrm{2m}} \:''\:\mathrm{in}\:\left(\mathrm{1}+\mathrm{a}\right)^{\mathrm{m}} \left(\mathrm{1}+\mathrm{b}\right)^{\mathrm{n}+\mathrm{m}} \left(\mathrm{1}+\mathrm{a}+\mathrm{b}\right)^{\mathrm{m}} . \\ $$

Question Number 155353 Answers: 2 Comments: 0

show that lim_(x→0) ((sinx)/x) = 1

$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \frac{\boldsymbol{{sinx}}}{\boldsymbol{{x}}}\:=\:\mathrm{1} \\ $$

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