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Question Number 74536 Answers: 1 Comments: 0

find limz⇒0 (xy^2 /x^2 +y^2 ) pleas sir help me

$${find}\:{limz}\Rightarrow\mathrm{0}\:\:\left({xy}^{\mathrm{2}} /{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\:{pleas}\:{sir}\:{help}\:{me}\: \\ $$

Question Number 74527 Answers: 2 Comments: 1

Question Number 74514 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) (((x−sinθ)dθ)/((x^2 −2x sinθ +1)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{\left({x}−{sin}\theta\right){d}\theta}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{sin}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 74513 Answers: 1 Comments: 1

find f(x)=∫_0 ^π (dθ/(x^2 −2xsin(2θ)+1)) (x real)

$${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{d}\theta}{{x}^{\mathrm{2}} −\mathrm{2}{xsin}\left(\mathrm{2}\theta\right)+\mathrm{1}}\:\:\left({x}\:{real}\right) \\ $$

Question Number 74526 Answers: 1 Comments: 0

prove that (1/2)tan^(−1) x=cos^(−1) ((√((1+(√(1+x^2 )))/(2(√(1+x^2 )))))) using substitution x=cos 2θ

$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{tan}^{−\mathrm{1}} {x}={cos}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}}\right) \\ $$$${using}\:{substitution}\:{x}={cos}\:\mathrm{2}\theta \\ $$

Question Number 74560 Answers: 0 Comments: 1

Question Number 74522 Answers: 0 Comments: 3

A rope inclined at angle 37° to the horizontal is used to drag a 50kg block along a level floor with an acceleration of 1m/s^2 .The coefficient of friction between the block and the floor is 0.2. What is the tension in the rope?

$${A}\:{rope}\:{inclined}\:{at}\:{angle}\:\mathrm{37}°\:{to}\:{the}\: \\ $$$${horizontal}\:{is}\:{used}\:{to}\:{drag}\:{a}\:\mathrm{50}{kg}\:{block} \\ $$$${along}\:{a}\:{level}\:{floor}\:{with}\:{an}\:{acceleration} \\ $$$${of}\:\mathrm{1}{m}/{s}^{\mathrm{2}} \:.{The}\:{coefficient}\:{of}\:{friction} \\ $$$${between}\:{the}\:{block}\:{and}\:{the}\:{floor}\:{is}\:\mathrm{0}.\mathrm{2}. \\ $$$${What}\:{is}\:{the}\:{tension}\:{in}\:{the}\:{rope}? \\ $$

Question Number 74520 Answers: 1 Comments: 0

Question Number 74515 Answers: 0 Comments: 0

Question Number 74508 Answers: 0 Comments: 0

li=x^− −t_v ,(α/2).((s/(√n))) ls=x^− +t_v ,(α/2).((s/(√n)))

$${li}=\overset{−} {{x}}−{t}_{{v}} ,\frac{\alpha}{\mathrm{2}}.\left(\frac{{s}}{\sqrt{{n}}}\right) \\ $$$${ls}=\overset{−} {{x}}+{t}_{{v}} ,\frac{\alpha}{\mathrm{2}}.\left(\frac{{s}}{\sqrt{{n}}}\right) \\ $$$$ \\ $$

Question Number 74502 Answers: 1 Comments: 4

let f(x)=e^(−nx) ln(1+x^2 ) 1)determine f^((n)) (x) and f^((n)) (0) 2)developp f at integr serie (n integr natural)

$${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right){determine}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:\:\:\left({n}\:{integr}\:{natural}\right) \\ $$

Question Number 74501 Answers: 0 Comments: 1

let P(x)=(1/(n!))(x^2 −1)^n calculate P^((n)) (x) and P^( (n)) (0)

$$\:{let}\:{P}\left({x}\right)=\frac{\mathrm{1}}{{n}!}\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} \\ $$$${calculate}\:{P}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{P}^{\:\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 74500 Answers: 0 Comments: 0

1) decompose the fraction F(x)=((x^3 −2)/((x+1)^4 (x−2)^3 )) 2)find ∫_3 ^(+∞) F(x)dx

$$\left.\mathrm{1}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{{x}^{\mathrm{3}} −\mathrm{2}}{\left({x}+\mathrm{1}\right)^{\mathrm{4}} \left({x}−\mathrm{2}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{2}\right){find}\:\:\:\int_{\mathrm{3}} ^{+\infty} \:{F}\left({x}\right){dx} \\ $$

Question Number 74499 Answers: 0 Comments: 1

decompose inside C(x) the fraction f(x)=(1/((x^2 +1)^n ))

$${decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fraction} \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$

Question Number 74498 Answers: 1 Comments: 1

1) calculte A_n =∫_0 ^∞ e^(−nx) [e^x ] dx with n integr and n≥2 2)find lim_(n→+∞) n^n A_n

$$\left.\mathrm{1}\right)\:{calculte}\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} \left[{e}^{{x}} \right]\:{dx}\:\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{n}^{{n}} \:{A}_{{n}} \\ $$

Question Number 74503 Answers: 0 Comments: 1

Question Number 74492 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(x^2 +9))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 74474 Answers: 1 Comments: 1

Question Number 74473 Answers: 1 Comments: 2

Question Number 74456 Answers: 1 Comments: 2

Question Number 74484 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(2x))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}}{dx} \\ $$

Question Number 74483 Answers: 1 Comments: 2

Question Number 74446 Answers: 1 Comments: 0

Question Number 74431 Answers: 0 Comments: 11

Question Number 74429 Answers: 0 Comments: 2

Question Number 74455 Answers: 1 Comments: 0

if K=(x∈R 2x−1+∣2x−1∣=0 )and J=(x∈R −x(2x+1)≤−1) find J−K.

$${if}\:{K}=\left({x}\in\mathbb{R}\:\mathrm{2}{x}−\mathrm{1}+\mid\mathrm{2}{x}−\mathrm{1}\mid=\mathrm{0}\:\right){and} \\ $$$${J}=\left({x}\in\mathbb{R}\:−{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\leqslant−\mathrm{1}\right)\:{find}\:{J}−{K}. \\ $$

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