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Question Number 170350    Answers: 0   Comments: 0

developpement limite de ordre 3 sin^2 x et cos^2 x

$${developpement}\:{limite}\:{de}\:{ordre}\:\mathrm{3} \\ $$$${sin}^{\mathrm{2}} {x}\:\:\:\:{et}\:\:\:{cos}^{\mathrm{2}} {x} \\ $$

Question Number 170349    Answers: 1   Comments: 0

help please ∫_1 ^∞ ((1/t)−sin^(−1) ((1/t))) dt I can show that it is equal to −Σ_(n≥0) (−1)^n (((2n−1)!)/(4^n (n!)^2 (2n+1))) but I cant calculate it...

$$ \\ $$$${help}\:{please}\:\: \\ $$$$\overset{\infty} {\int}_{\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}−\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{t}}\right)\right)\:{dt} \\ $$$${I}\:{can}\:{show}\:{that}\:{it}\:{is}\:{equal}\:{to} \\ $$$$−\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\mathrm{1}\right)^{{n}} \frac{\left(\mathrm{2}{n}−\mathrm{1}\right)!}{\mathrm{4}^{{n}} \left({n}!\right)^{\mathrm{2}} \left(\mathrm{2}{n}+\mathrm{1}\right)} \\ $$$${but}\:{I}\:{cant}\:{calculate}\:{it}... \\ $$

Question Number 170344    Answers: 1   Comments: 1

Is a semicircle a sector or a segment?

$${Is}\:{a}\:{semicircle}\:{a}\:{sector}\:{or}\:{a}\: \\ $$$${segment}? \\ $$

Question Number 170336    Answers: 2   Comments: 1

if cos^2 ∝ + 3cosec^2 θ = 7, find the expression of tan^2 θ, Hence show that tanθ=1. Mastermind

$${if}\:{cos}^{\mathrm{2}} \propto\:+\:\mathrm{3}{cosec}^{\mathrm{2}} \theta\:=\:\mathrm{7},\:{find}\:{the}\: \\ $$$${expression}\:{of}\:{tan}^{\mathrm{2}} \theta,\:{Hence}\:{show}\:{that} \\ $$$${tan}\theta=\mathrm{1}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170334    Answers: 0   Comments: 0

Question Number 170329    Answers: 1   Comments: 0

find the general solution of 1)y′′′−7y′+6y=x 2)y′′′−3y′′+2y′=(e^x /(1+e^(−x) ))

$${find}\:{the}\:{general}\:{solution}\:{of}\: \\ $$$$\left.\mathrm{1}\right){y}'''−\mathrm{7}{y}'+\mathrm{6}{y}={x} \\ $$$$\left.\mathrm{2}\right){y}'''−\mathrm{3}{y}''+\mathrm{2}{y}'=\frac{{e}^{{x}} }{\mathrm{1}+{e}^{−{x}} } \\ $$

Question Number 170327    Answers: 1   Comments: 0

Question Number 170323    Answers: 1   Comments: 0

Question Number 170322    Answers: 0   Comments: 0

Question Number 170321    Answers: 1   Comments: 0

Question Number 170318    Answers: 0   Comments: 0

Question Number 170305    Answers: 2   Comments: 0

A number with two digits is equal to four times the sum of its digits. The number formed by reversing the order of the digit is 27 greater than the given number. Find the number

$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{equal}}\:\boldsymbol{\mathrm{to}} \\ $$$$\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{times}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}.\:\boldsymbol{\mathrm{The}} \\ $$$$\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{formed}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{reversing}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{order}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{is}}\:\mathrm{27}\:\boldsymbol{\mathrm{greater}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{given}} \\ $$$$\boldsymbol{\mathrm{number}}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}} \\ $$

Question Number 170304    Answers: 0   Comments: 0

Question Number 170326    Answers: 0   Comments: 4

Is mass of a body greatest at the poles?. If yes or no, reason please? With diagram if possible. thanks

$$\boldsymbol{\mathrm{Is}}\:\boldsymbol{\mathrm{mass}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{body}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{poles}}?. \\ $$$$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{yes}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{no}},\:\boldsymbol{\mathrm{reason}}\:\boldsymbol{\mathrm{please}}? \\ $$$$\boldsymbol{\mathrm{With}}\:\boldsymbol{\mathrm{diagram}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{possible}}.\:\boldsymbol{\mathrm{thanks}} \\ $$

Question Number 170298    Answers: 0   Comments: 0

∫ (1/( ((1+x^4 ))^(1/4) ))dx

$$\int\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{1}+{x}^{\mathrm{4}} }}{dx} \\ $$

Question Number 170297    Answers: 1   Comments: 0

find the total charge enclosed inside a volume of 1.5×10^(−9) located at the origin if D=e^(−x) sin(y)a_x ^ −(e^(−x) cos(y))a_y ^ +2za^ z C/m^2

$$\:{find}\:{the}\:{total}\:{charge}\:{enclosed}\:{inside}\:{a}\: \\ $$$${volume}\:{of}\:\mathrm{1}.\mathrm{5}×\mathrm{10}^{−\mathrm{9}} \:{located}\:{at}\:{the}\:{origin} \\ $$$${if}\:{D}={e}^{−{x}} {sin}\left({y}\right)\hat {{a}}_{{x}} −\left({e}^{−{x}} {cos}\left({y}\right)\right)\hat {{a}}_{{y}} +\mathrm{2}{z}\hat {{a}z}\:{C}/{m}^{\mathrm{2}} \\ $$

Question Number 170294    Answers: 0   Comments: 0

Question Number 170292    Answers: 0   Comments: 0

Question Number 170290    Answers: 1   Comments: 1

Question Number 170289    Answers: 0   Comments: 0

Question Number 170288    Answers: 0   Comments: 0

Question Number 170287    Answers: 0   Comments: 0

Question Number 170284    Answers: 0   Comments: 6

Question Number 170276    Answers: 0   Comments: 1

Question Number 170275    Answers: 0   Comments: 0

Question Number 170270    Answers: 0   Comments: 3

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