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AllQuestion and Answers: Page 1081

Question Number 109497 Answers: 1 Comments: 0

Question Number 109495 Answers: 4 Comments: 0

1) ∫_0 ^(Π/2) sin x∙sin 2x∙sin 3x∙dx = ? 2) ∫_0 ^(1/2) arcsin x∙dx= ?

$$\left.\mathrm{1}\right)\:\:\:\:\int_{\mathrm{0}} ^{\frac{\Pi}{\mathrm{2}}} \mathrm{sin}\:{x}\centerdot\mathrm{sin}\:\mathrm{2}{x}\centerdot\mathrm{sin}\:\mathrm{3}{x}\centerdot{dx}\:=\:? \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \mathrm{arcsin}\:{x}\centerdot{dx}=\:? \\ $$

Question Number 109494 Answers: 2 Comments: 0

Question Number 109493 Answers: 1 Comments: 0

Question Number 109489 Answers: 2 Comments: 0

(1) sin (2x)−cos (2x)−sin (x)+cos (x)=0 (2)lim_(x→0) ((e^x −e^(−x) )/(sin x)) (3)lim_(x→−1) ∣x+1∣ sin (x+1)

$$\left(\mathrm{1}\right)\:\mathrm{sin}\:\left(\mathrm{2}{x}\right)−\mathrm{cos}\:\left(\mathrm{2}{x}\right)−\mathrm{sin}\:\left({x}\right)+\mathrm{cos}\:\left({x}\right)=\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{sin}\:{x}} \\ $$$$\left(\mathrm{3}\right)\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\mid{x}+\mathrm{1}\mid\:\mathrm{sin}\:\left({x}+\mathrm{1}\right) \\ $$$$ \\ $$

Question Number 109488 Answers: 0 Comments: 0

How many are the permutations of 1 − a little rubik′s cube with 4 squares by side 2 − a classical one with 9 squares by side

$${How}\:{many}\:{are}\:{the}\:{permutations}\:{of} \\ $$$$\mathrm{1}\:−\:{a}\:{little}\:{rubik}'{s}\:{cube}\:{with}\:\mathrm{4}\:{squares}\:{by}\:{side} \\ $$$$\mathrm{2}\:−\:{a}\:{classical}\:{one}\:{with}\:\mathrm{9}\:{squares}\:{by}\:{side} \\ $$

Question Number 109485 Answers: 1 Comments: 0

If f(x)=ax^2 +bx+c, g(x)= −ax^2 +bx+c where ac ≠ 0, then f(x)g(x)=0 has

$$\mathrm{If}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c},\:{g}\left({x}\right)=\:−{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$$\mathrm{where}\:{ac}\:\neq\:\mathrm{0},\:\mathrm{then}\:{f}\left({x}\right){g}\left({x}\right)=\mathrm{0}\:\mathrm{has} \\ $$

Question Number 109483 Answers: 1 Comments: 2

Question Number 109472 Answers: 4 Comments: 0

Question Number 109469 Answers: 0 Comments: 2

Question Number 109468 Answers: 0 Comments: 0

Question Number 109464 Answers: 0 Comments: 0

(√(1+(√(2+(√(3+(√(4+...))))))))

$$\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+...}}}} \\ $$

Question Number 109463 Answers: 0 Comments: 3

Question Number 109462 Answers: 1 Comments: 0

Question Number 109461 Answers: 1 Comments: 0

Question Number 109460 Answers: 1 Comments: 0

Question Number 109459 Answers: 0 Comments: 0

Question Number 109457 Answers: 3 Comments: 0

Question Number 109453 Answers: 1 Comments: 0

Question Number 109470 Answers: 0 Comments: 1

Question Number 109435 Answers: 1 Comments: 0

Question Number 109428 Answers: 2 Comments: 2

Question Number 109427 Answers: 1 Comments: 0

Question Number 109414 Answers: 2 Comments: 0

Question Number 109410 Answers: 3 Comments: 1

solve { ((x≡3 (mod 5))),((x≡ 1 (mod 7))),((x ≡ 6 (mod 8))) :}

$${solve}\:\begin{cases}{{x}\equiv\mathrm{3}\:\left({mod}\:\mathrm{5}\right)}\\{{x}\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{7}\right)}\\{{x}\:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{8}\right)}\end{cases} \\ $$

Question Number 109403 Answers: 2 Comments: 0

∫ (dx/( (√(x^2 +a^2 ))))=ln∣x+(√(x^2 +a^2 ))∣+C Proof?

$$\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }}=\mathrm{ln}\mid\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }\mid+{C}\:\:\:\:\mathrm{Proof}? \\ $$

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