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Question Number 10913 Answers: 1 Comments: 0

∫_( 1) ^( 3) x^x dx

$$\int_{\:\mathrm{1}} ^{\:\mathrm{3}} \:\mathrm{x}^{\mathrm{x}} \:\:\mathrm{dx} \\ $$

Question Number 10912 Answers: 0 Comments: 1

5^(log_2 3) is transcendental? General: Let a,b and c algebraic and log_b c transcendental. If a^(log_b c) is algebraic, so b = a^q , with q rational?

$$\mathrm{5}^{\mathrm{log}_{\mathrm{2}} \mathrm{3}} \:\mathrm{is}\:\mathrm{transcendental}? \\ $$$$\mathrm{General}: \\ $$$$\mathrm{Let}\:{a},{b}\:\mathrm{and}\:{c}\:\mathrm{algebraic}\:\mathrm{and}\:\mathrm{log}_{{b}} {c}\: \\ $$$$\mathrm{transcendental}.\:\mathrm{If}\:{a}^{\mathrm{log}_{{b}} {c}} \:\mathrm{is}\:\mathrm{algebraic},\:\mathrm{so} \\ $$$${b}\:=\:{a}^{{q}} ,\:\mathrm{with}\:{q}\:\mathrm{rational}? \\ $$

Question Number 10908 Answers: 1 Comments: 0

Question Number 10907 Answers: 1 Comments: 0

express in partial fraction ((3x+2)/((x^2 −1)(x+1)))

$$\mathrm{express}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction} \\ $$$$\frac{\mathrm{3x}+\mathrm{2}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)} \\ $$

Question Number 10906 Answers: 1 Comments: 1

Q . smallest positive x satisfying the equation sin3x+3cosx=2sin2x(sinx+cosx) , is

$${Q}\:.\:\:{smallest}\:{positive}\:{x}\:{satisfying}\:{the}\:{equation} \\ $$$${sin}\mathrm{3}{x}+\mathrm{3}{cosx}=\mathrm{2}{sin}\mathrm{2}{x}\left({sinx}+{cosx}\right)\:,\:{is} \\ $$

Question Number 10903 Answers: 0 Comments: 0

Question Number 10902 Answers: 2 Comments: 0

∫(√(1−x^2 ))dx=?

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 10900 Answers: 0 Comments: 1

Question Number 10899 Answers: 1 Comments: 0

Question Number 10898 Answers: 1 Comments: 0

Question Number 10887 Answers: 1 Comments: 0

Suppose that f(x) = (1/(x + 1)) and g(x) = (4/(x + 1)) . Find the domain of each of the composition (a) f o g (b) f o f

$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}\:+\:\mathrm{1}}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4}}{\mathrm{x}\:+\:\mathrm{1}}\:. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{composition}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{f}\:\mathrm{o}\:\mathrm{g}\:\:\:\left(\mathrm{b}\right)\:\:\mathrm{f}\:\mathrm{o}\:\mathrm{f} \\ $$

Question Number 10880 Answers: 1 Comments: 0

∫ (x + 3)(√((x + 4))) dx

$$\left.\int\:\left(\mathrm{x}\:+\:\mathrm{3}\right)\sqrt{\left(\mathrm{x}\:+\:\mathrm{4}\right.}\right)\:\mathrm{dx}\: \\ $$

Question Number 10876 Answers: 1 Comments: 0

∫_( 0) ^( 1) ∫_( x) ^( (√x)) (x + y^5 ) dy dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \int_{\:\mathrm{x}} ^{\:\sqrt{\mathrm{x}}} \:\left(\mathrm{x}\:+\:\mathrm{y}^{\mathrm{5}} \right)\:\mathrm{dy}\:\mathrm{dx} \\ $$

Question Number 10889 Answers: 0 Comments: 0

The solution of the Schanuel′s Conjecture will to decide if γ is transcendental or not? Tell me all consequences of the conjecture.

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Schanuel}'\mathrm{s}\:\mathrm{Conjecture} \\ $$$$\mathrm{will}\:\mathrm{to}\:\mathrm{decide}\:\mathrm{if}\:\gamma\:\mathrm{is}\:\mathrm{transcendental}\:\mathrm{or}\:\mathrm{not}? \\ $$$$\mathrm{Tell}\:\mathrm{me}\:\mathrm{all}\:\mathrm{consequences}\:\mathrm{of}\:\mathrm{the}\:\mathrm{conjecture}. \\ $$

Question Number 10874 Answers: 1 Comments: 0

If f(x + 3) = 2x^2 − 3x + 5. find f(5)

$$\mathrm{If}\:\:\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{3}\right)\:=\:\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{5}.\:\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{5}\right) \\ $$

Question Number 10872 Answers: 1 Comments: 0

In a cultural gathering of 400 people, there are 270 men and 200 musicians. Of the latter, 80 are singers. 60 of the women are not musicians and 220 of the men are not singers. How many of the women are musicians but not singers. if there are 150 singers altogether and 40 men are both musicians and singers.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{cultural}\:\mathrm{gathering}\:\mathrm{of}\:\mathrm{400}\:\mathrm{people},\:\mathrm{there}\:\mathrm{are}\:\mathrm{270}\:\mathrm{men}\:\mathrm{and}\:\mathrm{200} \\ $$$$\mathrm{musicians}.\:\mathrm{Of}\:\mathrm{the}\:\mathrm{latter},\:\mathrm{80}\:\mathrm{are}\:\mathrm{singers}.\:\mathrm{60}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are}\:\mathrm{not}\:\:\mathrm{musicians} \\ $$$$\mathrm{and}\:\mathrm{220}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{are}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are} \\ $$$$\mathrm{musicians}\:\mathrm{but}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{150}\:\mathrm{singers}\:\mathrm{altogether}\:\mathrm{and}\: \\ $$$$\mathrm{40}\:\mathrm{men}\:\mathrm{are}\:\mathrm{both}\:\mathrm{musicians}\:\mathrm{and}\:\mathrm{singers}. \\ $$

Question Number 10873 Answers: 1 Comments: 0

without using calculator or table, find the exact value of : sin[tan^(−1) ((1/2))]

$$\mathrm{without}\:\mathrm{using}\:\mathrm{calculator}\:\mathrm{or}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of}\:\:: \\ $$$$\mathrm{sin}\left[\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\right] \\ $$

Question Number 10868 Answers: 0 Comments: 0

Question Number 10867 Answers: 0 Comments: 0

(1) Show that : ((x^(2n + 1) − y^(2n + 1) )/(x − y)) = x^(2n ) + x^(2n − 1) y + ... + xy^(2n − 1) + y^(2n) (2) Show that: ((x^(2n) − y^(2n) )/(x − y)) = x^(2n − 1 ) + x^(2n − 2) y + ... + xy^(2n − 2) + y^(2n − 1)

$$\left(\mathrm{1}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}\:: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}\:+\:\mathrm{1}} \:−\:\mathrm{y}^{\mathrm{2n}\:+\:\mathrm{1}} }{\mathrm{x}\:−\:\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2n}\:} +\:\mathrm{x}^{\mathrm{2n}\:−\:\mathrm{1}} \mathrm{y}\:+\:...\:+\:\mathrm{xy}^{\mathrm{2n}\:−\:\mathrm{1}} \:+\:\mathrm{y}^{\mathrm{2n}} \\ $$$$\left(\mathrm{2}\right) \\ $$$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{2n}} \:−\:\mathrm{y}^{\mathrm{2n}} }{\mathrm{x}\:−\:\mathrm{y}}\:=\:\mathrm{x}^{\mathrm{2n}\:\:−\:\mathrm{1}\:} +\:\mathrm{x}^{\mathrm{2n}\:−\:\mathrm{2}} \mathrm{y}\:+\:...\:+\:\mathrm{xy}^{\mathrm{2n}\:−\:\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2n}\:−\:\mathrm{1}} \\ $$

Question Number 10865 Answers: 0 Comments: 0