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AllQuestion and Answers: Page 1104

Question Number 107230 Answers: 0 Comments: 0

Question Number 107222 Answers: 5 Comments: 0

Question Number 107212 Answers: 4 Comments: 0

⊚bemath⊚ ∫ x^6 (√(1−x^2 )) dx ?

$$\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\int\:{x}^{\mathrm{6}} \:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 107207 Answers: 4 Comments: 0

⊚bemath⊚ lim_(x→∞) (2^x +3^x )^(1/x) ?

$$\:\:\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}^{{x}} +\mathrm{3}^{{x}} \right)^{\frac{\mathrm{1}}{{x}}} \:?\: \\ $$

Question Number 107202 Answers: 2 Comments: 0

Question Number 107238 Answers: 3 Comments: 0

⊞bemath⊞ ∫ ((sin x)/(sin^3 x+cos^3 x)) dx ?

$$\:\:\:\:\:\:\:\boxplus{bemath}\boxplus \\ $$$$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x}}\:{dx}\:?\: \\ $$

Question Number 107198 Answers: 1 Comments: 2

Solve the given equation: (x+(x/3^1 ))∙(x+(x/3^2 ))∙(x+(x/3^3 ))∙(x+(x/3^4 ))∙...∙(x+(x/3^(25) ))=1 A)(3^(51) /(2∙(3^(50) −1))) B)(3^(52) /(2∙(3^(51) −1))) C) (3^(50) /(2∙(3^(50) −1))) D) (3^(51) /(3^(51) −1)) Please help with solution

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{given}\:\mathrm{equation}: \\ $$$$\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{1}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{2}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{3}} }\right)\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{4}} }\right)\centerdot...\centerdot\left(\mathrm{x}+\frac{\mathrm{x}}{\mathrm{3}^{\mathrm{25}} }\right)=\mathrm{1} \\ $$$$\left.\mathrm{A}\left.\right)\left.\frac{\mathrm{3}^{\mathrm{51}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{50}} −\mathrm{1}\right)}\left.\:\:\mathrm{B}\right)\frac{\mathrm{3}^{\mathrm{52}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{51}} −\mathrm{1}\right)}\:\:\mathrm{C}\right)\:\frac{\mathrm{3}^{\mathrm{50}} }{\mathrm{2}\centerdot\left(\mathrm{3}^{\mathrm{50}} −\mathrm{1}\right)}\:\:\mathrm{D}\right)\:\frac{\mathrm{3}^{\mathrm{51}} }{\mathrm{3}^{\mathrm{51}} −\mathrm{1}} \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{solution} \\ $$

Question Number 107197 Answers: 0 Comments: 0

⊵JS⊴ ∫ _0 ^( π/6) sin^2 (6x) cos^4 (3x) dx ? [ by using the Gamma function ]

$$\:\:\:\:\:\trianglerighteq\mathrm{JS}\trianglelefteq \\ $$$$\int\overset{\:\pi/\mathrm{6}} {\:}_{\mathrm{0}} \mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{6x}\right)\:\mathrm{cos}\:^{\mathrm{4}} \left(\mathrm{3x}\right)\:\mathrm{dx}\:? \\ $$$$\left[\:\mathrm{by}\:\mathrm{using}\:\mathrm{the}\:\mathcal{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$

Question Number 107196 Answers: 2 Comments: 8

How many different words can be formed with the same letters as in TINKUTARA if no two same letters are next to each other.

$${How}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{same}\:{letters}\:{as}\:{in} \\ $$$${TINKUTARA}\:{if}\:{no}\:{two}\:{same}\:{letters} \\ $$$${are}\:{next}\:{to}\:{each}\:{other}. \\ $$

Question Number 107193 Answers: 1 Comments: 0

∫_0 ^4 ((ln x)/(√(4x−x^2 ))) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\sqrt{\mathrm{4x}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$

Question Number 107187 Answers: 1 Comments: 3

Prove that (√8)=1+(3/4)+((3.5)/(4.8))+((3.5.7)/(4.8.12))+......