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AllQuestion and Answers: Page 26

Question Number 222072 Answers: 1 Comments: 2

Question Number 222064 Answers: 0 Comments: 3

Question Number 222066 Answers: 0 Comments: 4

Question Number 222057 Answers: 0 Comments: 2

lim_(n→∞) ((1^1 ×2^2 ×3^3 ......×n^n )/(n^((1/2)n^2 +(1/2)n^2 +(1/(12))) ×e^(−(1/4)n^2 ) ))=??? Help.... i can′t Solve that lim_(n→∞) a_n ...

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}^{\mathrm{1}} ×\mathrm{2}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{3}} ......×{n}^{{n}} }{{n}^{\frac{\mathrm{1}}{\mathrm{2}}{n}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{n}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{12}}} ×{e}^{−\frac{\mathrm{1}}{\mathrm{4}}{n}^{\mathrm{2}} } }=??? \\ $$$$\mathrm{Help}.... \\ $$$$\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{Solve}\:\mathrm{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} ... \\ $$

Question Number 222062 Answers: 2 Comments: 0

Question Number 222044 Answers: 1 Comments: 0

How do you evaluate ∫_(−∞) ^( ∞) ((sin(z+1))/((z+1)(z^2 +1))) dz

$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{evaluate} \\ $$$$\int_{−\infty} ^{\:\:\infty} \:\:\frac{\mathrm{sin}\left({z}+\mathrm{1}\right)}{\left({z}+\mathrm{1}\right)\left({z}^{\mathrm{2}} +\mathrm{1}\right)}\:\mathrm{d}{z} \\ $$

Question Number 222031 Answers: 3 Comments: 0

x^x =−1 Number of solutions??

$${x}^{{x}} =−\mathrm{1} \\ $$$${Number}\:{of}\:{solutions}?? \\ $$

Question Number 222026 Answers: 2 Comments: 0

If (1.234)^a =(0.1234)^b =10^c prove that (1/a)−(1/c)=(1/b)

$${If}\:\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}} =\mathrm{10}^{{c}} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{a}}−\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{{b}} \\ $$

Question Number 222025 Answers: 1 Comments: 0

(((5cos^2 (π/3)+4sec^2 (π/6)−tan^2 (π/4))/(sin^2 (π/6)+cos^2 (π/6))))=?? [easy mode]

$$\left(\frac{\mathrm{5cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{3}}+\mathrm{4sec}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}−\mathrm{tan}\:^{\mathrm{2}} \frac{\pi}{\mathrm{4}}}{\mathrm{sin}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}+\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}}\right)=?? \\ $$$$\left[{easy}\:{mode}\right] \\ $$

Question Number 222022 Answers: 1 Comments: 2

If ∠P+∠Q =90^0 then prove that (√(((sin P)/(cos Q))−sin Pcos Q))=cos P

$${If}\:\angle{P}+\angle{Q}\:=\mathrm{90}^{\mathrm{0}} \:{then}\:{prove}\:{that} \\ $$$$\sqrt{\frac{\mathrm{sin}\:{P}}{\mathrm{cos}\:{Q}}−\mathrm{sin}\:{P}\mathrm{cos}\:{Q}}=\mathrm{cos}\:{P} \\ $$

Question Number 222019 Answers: 0 Comments: 0

∫_0 ^π tan^(−1) (((ln(sin(x))/x)) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi} \:\mathrm{tan}^{−\mathrm{1}} \:\left(\frac{\mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right.}{{x}}\right)\:{dx} \\ $$$$ \\ $$

Question Number 222007 Answers: 0 Comments: 5

x(√(1+x^2 ))+log(x+(√(1+x^2 )))=12.5 find x^2 (answer should not be in decimal)

$$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$

Question Number 222003 Answers: 2 Comments: 0

If a+b+c=0 then prove that (1/(x^b +x^(−c) +1))+(1/(x^c +x^(−a) +1))+(1/(x^a +x^(−b) +1))=1

$${If}\:{a}+{b}+{c}=\mathrm{0}\:{then}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{x}^{{b}} +{x}^{−{c}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{c}} +{x}^{−{a}} +\mathrm{1}}+\frac{\mathrm{1}}{{x}^{{a}} +{x}^{−{b}} +\mathrm{1}}=\mathrm{1} \\ $$

Question Number 222001 Answers: 1 Comments: 6

(((4^(m+(1/4)) ×(√(2.2^m )))/(2.(√2^(−m) ))))^(1/m) =??

$$\left(\frac{\mathrm{4}^{{m}+\frac{\mathrm{1}}{\mathrm{4}}} ×\sqrt{\mathrm{2}.\mathrm{2}^{{m}} }}{\mathrm{2}.\sqrt{\mathrm{2}^{−{m}} }}\right)^{\frac{\mathrm{1}}{{m}}} =?? \\ $$

Question Number 221991 Answers: 1 Comments: 4

Simplify: 2^2 ∙ 2^(2^((70 − t_1 )/(10)) = ?)

$$\mathrm{Simplify}:\:\:\:\mathrm{2}^{\mathrm{2}} \:\centerdot\:\mathrm{2}^{\mathrm{2}^{\frac{\mathrm{70}\:−\:\boldsymbol{\mathrm{t}}_{\mathrm{1}} }{\mathrm{10}}} \:\:\:=\:\:\:?} \\ $$

Question Number 221981 Answers: 0 Comments: 0

Prove:Σ_(n=1) ^∞ (n^3 /(e^(2πn) −1))=((Γ((1/4))^8 )/(5120π^6 ))−(1/(240))=(1/(80))((ϖ/π))^4 −(1/(240))

$$\mathrm{Prove}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{3}} }{{e}^{\mathrm{2}\pi{n}} −\mathrm{1}}=\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{8}} }{\mathrm{5120}\pi^{\mathrm{6}} }−\frac{\mathrm{1}}{\mathrm{240}}=\frac{\mathrm{1}}{\mathrm{80}}\left(\frac{\varpi}{\pi}\right)^{\mathrm{4}} −\frac{\mathrm{1}}{\mathrm{240}} \\ $$

Question Number 221973 Answers: 1 Comments: 0

(d^2 y/dx^2 )+y=k−(1/x^2 )−(6/x^4 ) Find y(x) (k is constant).

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{y}={k}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\frac{\mathrm{6}}{{x}^{\mathrm{4}} }\:\:\:\:\:\: \\ $$$${Find}\:{y}\left({x}\right)\:\:\:\:\left({k}\:{is}\:{constant}\right). \\ $$

Question Number 221968 Answers: 3 Comments: 0

(a+b+c)^3

$$\left({a}+{b}+{c}\right)^{\mathrm{3}} \\ $$

Question Number 221962 Answers: 0 Comments: 0

Question Number 221959 Answers: 0 Comments: 4

A bag contains 5 identical balls of which there is one red, one blue and the rest are white. What is the probability of selecting at least one white balls, if 3 balls are selected.

Question Number 221958 Answers: 1 Comments: 2

Question Number 221957 Answers: 2 Comments: 0

∫sin^(−1) (cos x)dx

$$\int\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{cos}\:{x}\right){dx} \\ $$

Question Number 221955 Answers: 0 Comments: 0

∫_0 ^∞ tan^(−1) (((ln(sin (x))/x)) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{ln}\left(\mathrm{sin}\:\left({x}\right)\right.}{{x}}\right)\:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 221944 Answers: 1 Comments: 1

Question Number 221943 Answers: 1 Comments: 0

Question Number 221939 Answers: 2 Comments: 1

sin^2 1° + sin^2 3° + sin^2 5° + ... + sin^2 269° = ? Help me, please

$$ \\ $$$$\:\:\:{sin}^{\mathrm{2}} \mathrm{1}°\:+\:{sin}^{\mathrm{2}} \mathrm{3}°\:+\:{sin}^{\mathrm{2}} \mathrm{5}°\:+\:...\:+\:{sin}^{\mathrm{2}} \mathrm{269}°\:=\:? \\ $$$$\:\:\:\mathcal{H}{elp}\:{me},\:\:{please} \\ $$$$ \\ $$

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