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Question Number 99681 Answers: 1 Comments: 0

Question Number 99680 Answers: 0 Comments: 0

Question Number 99679 Answers: 0 Comments: 1

Question Number 99677 Answers: 0 Comments: 0

Question Number 99676 Answers: 1 Comments: 0

lim_(x→0) ((sin (sin x)−x)/(x(cos (sin x)−1)))??

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}}{\mathrm{x}\left(\mathrm{cos}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{1}\right)}?? \\ $$

Question Number 99670 Answers: 0 Comments: 2

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Question Number 99667 Answers: 0 Comments: 0

State and prove the fundamental theorem of intergral calculus

$$\mathrm{State}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{fundamental}\:\mathrm{theorem} \\ $$$$\mathrm{of}\:\mathrm{intergral}\:\mathrm{calculus} \\ $$

Question Number 99666 Answers: 0 Comments: 0

Question Number 99665 Answers: 0 Comments: 1

Question Number 99661 Answers: 0 Comments: 0

Question Number 99655 Answers: 1 Comments: 1

Question Number 99646 Answers: 2 Comments: 0

use power series solution method to solve the ODE y′′−xy=0

$$\boldsymbol{{use}}\:\boldsymbol{{power}}\:\boldsymbol{{series}}\:\boldsymbol{{solution}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{ODE}} \\ $$$$\boldsymbol{{y}}''−\boldsymbol{{xy}}=\mathrm{0} \\ $$

Question Number 99645 Answers: 1 Comments: 1

If x,y > 0 then ∣(√(xy))−((x+y)/2)∣ + ∣((x+y)/2) + (√(xy)) ∣ =

$${If}\:{x},{y}\:>\:\mathrm{0}\:{then}\:\mid\sqrt{{xy}}−\frac{{x}+{y}}{\mathrm{2}}\mid\:+\:\mid\frac{{x}+{y}}{\mathrm{2}}\:+\:\sqrt{{xy}}\:\mid\:= \\ $$

Question Number 99623 Answers: 1 Comments: 1

obtain the modulus and arguement of (((1−i)^4 )/((2+2(√(3i)^3 ))))

$${obtain}\:{the}\:{modulus}\:{and}\:{arguement}\:{of} \\ $$$$\frac{\left(\mathrm{1}−{i}\right)^{\mathrm{4}} }{\left(\mathrm{2}+\mathrm{2}\sqrt{\left.\mathrm{3}{i}\right)^{\mathrm{3}} }\right.} \\ $$

Question Number 99621 Answers: 2 Comments: 1

6^x =x^(5 ) x=? help me

$$\mathrm{6}^{\mathrm{x}} =\mathrm{x}^{\mathrm{5}\:\:\:\:\:\:\:} \mathrm{x}=?\:\:\:\:\:\:\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 99620 Answers: 1 Comments: 1

If α=((2π)/7) then what is the value of (sinαsin2αsin4α)

$${If}\:\:\alpha=\frac{\mathrm{2}\pi}{\mathrm{7}}\:\:{then}\:{what}\:{is}\:{the}\:{value}\:{of}\:\left({sin}\alpha{sin}\mathrm{2}\alpha{sin}\mathrm{4}\alpha\right) \\ $$

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Question Number 99612 Answers: 0 Comments: 1

Question Number 99606 Answers: 0 Comments: 1

Question Number 99603 Answers: 1 Comments: 2

How many terms in the geometric progression 1, 1.1, 1.21,1.331,... will be needed so that the sum of the first n terms is greather than 20?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the}\:\mathrm{geometric} \\ $$$$\mathrm{progression}\:\mathrm{1},\:\mathrm{1}.\mathrm{1},\:\mathrm{1}.\mathrm{21},\mathrm{1}.\mathrm{331},... \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{needed}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{greather}\:\mathrm{than}\:\mathrm{20}? \\ $$

Question Number 99600 Answers: 1 Comments: 0

Question Number 99584 Answers: 1 Comments: 0

Question Number 99580 Answers: 4 Comments: 1

let A = (((2 −1)),((3 1)) ) 1) prove that A is inversible and calculste A^(−1) 2) calculate A^n 3) find e^A and e^(−A) 4) calculate cos A and sinA is cos^2 A +sin^2 A = I ?

$$\mathrm{let}\:\mathrm{A}\:=\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{prove}\:\mathrm{that}\:\mathrm{A}\:\mathrm{is}\:\mathrm{inversible}\:\mathrm{and}\:\mathrm{calculste}\:\mathrm{A}^{−\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{A}^{\mathrm{n}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{e}^{\mathrm{A}} \:\mathrm{and}\:\mathrm{e}^{−\mathrm{A}} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{calculate}\:\mathrm{cos}\:\mathrm{A}\:\mathrm{and}\:\mathrm{sinA}\:\:\:\mathrm{is}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{A}\:+\mathrm{sin}^{\mathrm{2}} \:\mathrm{A}\:=\:\mathrm{I}\:? \\ $$$$ \\ $$

Question Number 99578 Answers: 2 Comments: 0

1)calculate U_n =∫_0 ^∞ e^(−nx^4 ) dx and determine lim_(n→+∞) n^4 U_n 2) find nature of the serie Σ U_n

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{nx}^{\mathrm{4}} } \mathrm{dx}\:\:\mathrm{and}\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{n}^{\mathrm{4}} \:\mathrm{U}_{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{serie}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$

Question Number 99576 Answers: 2 Comments: 0

1)let f(a) =∫_0 ^∞ (( t^(a−1) ln(t))/(1+t)) dt with 0<a<1 prove that f(a)is convergent and determine it value 2)calculate∫_0 ^∞ ((lnt)/((1+t)(√t)))dt 3)calculate∫_0 ^∞ ((lnt)/((^3 (√t^2 ))(1+t)))dt

$$\left.\mathrm{1}\right)\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:\mathrm{t}^{\mathrm{a}−\mathrm{1}} \mathrm{ln}\left(\mathrm{t}\right)}{\mathrm{1}+\mathrm{t}}\:\mathrm{dt}\:\:\:\mathrm{with}\:\mathrm{0}<\mathrm{a}<\mathrm{1}\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{a}\right)\mathrm{is}\:\mathrm{convergent}\:\mathrm{and}\:\mathrm{determine} \\ $$$$\mathrm{it}\:\mathrm{value} \\ $$$$\left.\mathrm{2}\right)\mathrm{calculate}\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnt}}{\left(\mathrm{1}+\mathrm{t}\right)\sqrt{\mathrm{t}}}\mathrm{dt} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculate}\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnt}}{\left(^{\mathrm{3}} \sqrt{\mathrm{t}^{\mathrm{2}} }\right)\left(\mathrm{1}+\mathrm{t}\right)}\mathrm{dt} \\ $$

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