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Question Number 111442    Answers: 3   Comments: 0

lim_(x→∞) (((x+a)/(x−a)))^x ?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}−\mathrm{a}}\right)^{\mathrm{x}} ? \\ $$

Question Number 111441    Answers: 1   Comments: 0

solve { ((y′′ −2y′+2y=sinht)),((y′(0)=1 , y(0)=1)) :}

$${solve} \\ $$$$ \\ $$$$\begin{cases}{{y}''\:−\mathrm{2}{y}'+\mathrm{2}{y}={sinht}}\\{{y}'\left(\mathrm{0}\right)=\mathrm{1}\:,\:{y}\left(\mathrm{0}\right)=\mathrm{1}}\end{cases} \\ $$

Question Number 111432    Answers: 2   Comments: 2

Question Number 111429    Answers: 1   Comments: 0

please evaluate : .... I=∫_0 ^( (π/2)) ((1/(ln(tan(x)))) + (1/(1−tan(x))))dx =??? ::: M. N.july 1970 :::

$$\:\:\:\:\:\:{please}\:\:{evaluate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:....\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\frac{\mathrm{1}}{{ln}\left({tan}\left({x}\right)\right)}\:+\:\frac{\mathrm{1}}{\mathrm{1}−{tan}\left({x}\right)}\right){dx}\:=??? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\::::\:\:\:\:\mathscr{M}.\:\mathscr{N}.{july}\:\mathrm{1970}\:::: \\ $$$$\:\: \\ $$

Question Number 111428    Answers: 0   Comments: 1

Σ_(n=1) ^∞ (n^3 /(n!))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{3}} }{{n}!} \\ $$

Question Number 111427    Answers: 0   Comments: 1

4sin^6 α + 4cos^6 α − 3cos^2 2α

$$\mathrm{4sin}\:^{\mathrm{6}} \alpha\:+\:\mathrm{4cos}\:^{\mathrm{6}} \alpha\:−\:\mathrm{3cos}\:^{\mathrm{2}} \mathrm{2}\alpha \\ $$

Question Number 111426    Answers: 2   Comments: 0

Question Number 111414    Answers: 2   Comments: 0

(1) lim_(x→0) ((sin x−ln (e^x cos x))/(x sin x)) (2) lim_(x→1) ((1−x+ln (x))/(1−(√(2x−x^2 ))))

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

Question Number 111393    Answers: 0   Comments: 6

What is the sum of the coefficients in the expansion of (2015v−2015u+1)^(2015) ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{2015v}−\mathrm{2015u}+\mathrm{1}\right)^{\mathrm{2015}} ? \\ $$

Question Number 111394    Answers: 1   Comments: 2

A teacher conducts a test for five students. He provides the marking scheme and asked them to exchange their scripts such that none of them marks his own script. How many ways can the students carry out the marking?

$$\mathrm{A}\:\mathrm{teacher}\:\mathrm{conducts}\:\mathrm{a}\:\mathrm{test}\:\mathrm{for}\:\mathrm{five} \\ $$$$\mathrm{students}.\:\mathrm{He}\:\mathrm{provides}\:\mathrm{the}\:\mathrm{marking} \\ $$$$\mathrm{scheme}\:\mathrm{and}\:\mathrm{asked}\:\mathrm{them}\:\mathrm{to}\:\mathrm{exchange} \\ $$$$\mathrm{their}\:\mathrm{scripts}\:\mathrm{such}\:\mathrm{that}\:\mathrm{none}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{marks}\:\mathrm{his}\:\mathrm{own}\:\mathrm{script}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways} \\ $$$$\mathrm{can}\:\mathrm{the}\:\mathrm{students}\:\mathrm{carry}\:\mathrm{out}\:\mathrm{the} \\ $$$$\mathrm{marking}? \\ $$

Question Number 111391    Answers: 2   Comments: 0

Compute cos(Π/(12))

$$\mathrm{Compute}\:\mathrm{cos}\frac{\Pi}{\mathrm{12}} \\ $$

Question Number 111388    Answers: 0   Comments: 0

Question Number 111397    Answers: 1   Comments: 2

lim_(x→0) ((cosx)/x)=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cosx}}{\mathrm{x}}=? \\ $$

Question Number 111383    Answers: 1   Comments: 0

lim_(s→∞) (√(20s^2 +2s))−(√(5s^2 +1))−(√(5s^2 −2s))

$$\:\:\underset{{s}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{20}{s}^{\mathrm{2}} +\mathrm{2}{s}}−\sqrt{\mathrm{5}{s}^{\mathrm{2}} +\mathrm{1}}−\sqrt{\mathrm{5}{s}^{\mathrm{2}} −\mathrm{2}{s}} \\ $$

Question Number 111382    Answers: 2   Comments: 1

Question Number 111377    Answers: 0   Comments: 0

A baggage tractor pulling luggage carts from an airplane. The tractor has mass 6500 kg while cart A has mass 2500 kg and cart B has mass 150 kg. The driving force acting for a brief period of time accelerates the system from rest and acts for 3s. (a) If this driving force is given by F=820N. find the speed after 3s (b) Wat is the horizontal force acting on the conneting cable between the tractor and cart A at this instant

$$ \\ $$$$\mathrm{A}\:\mathrm{baggage}\:\mathrm{tractor}\:\mathrm{pulling}\:\mathrm{luggage}\:\mathrm{carts}\:\mathrm{fro}{m}\:{an} \\ $$$$\:\mathrm{airplane}.\:\mathrm{The}\:\mathrm{tractor}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{6500}\:\mathrm{kg}\:\mathrm{while} \\ $$$${c}\mathrm{art}\:\mathrm{A}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{2500}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{cart}\:\mathrm{B}\:\mathrm{has}\:\mathrm{mass} \\ $$$$\mathrm{150}\:\mathrm{kg}.\:\mathrm{The}\:\mathrm{driving}\:\mathrm{force}\:\mathrm{acting}\:\mathrm{for}\:\mathrm{a}\:\mathrm{brief} \\ $$$$\mathrm{perio}{d}\:\mathrm{of}\:\mathrm{time}\:\mathrm{accelerates}\:\mathrm{the}\:\mathrm{system}\:\mathrm{from}\:\mathrm{rest} \\ $$$$\mathrm{a}{n}\mathrm{d}\:\mathrm{acts}\:\mathrm{for}\:\mathrm{3}{s}.\:\left(\mathrm{a}\right)\:\mathrm{If}\:\mathrm{this}\:\mathrm{driving}\:\mathrm{force}\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{b}{y}\:\mathrm{F}=\mathrm{820}{N}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{after}\:\mathrm{3}{s}\:\left({b}\right) \\ $$$$\mathrm{Wat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{force}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{conneting}\:\mathrm{cable}\:\mathrm{between}\:\mathrm{the}\:\mathrm{tractor}\:\mathrm{and}\:\mathrm{cart}\:\:{A}\: \\ $$$$\mathrm{at}\:\mathrm{this}\:\mathrm{instant} \\ $$

Question Number 111374    Answers: 1   Comments: 1

Question Number 111365    Answers: 0   Comments: 0

Question Number 111471    Answers: 0   Comments: 0

using power expension, compute the follplowing limit as a function of α>0 lim_(x→0^+ ) ((x^(7/2) ln(x)−sinh(x^2 )+cosh(ln(1−(√2)x))−1)/x^α )

$${using}\:{power}\:{expension},\:{compute}\:{the}\:{follplowing} \\ $$$${limit}\:{as}\:{a}\:{function}\:{of}\:\alpha>\mathrm{0} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{{x}^{\frac{\mathrm{7}}{\mathrm{2}}} {ln}\left({x}\right)−{sinh}\left({x}^{\mathrm{2}} \right)+{cosh}\left({ln}\left(\mathrm{1}−\sqrt{\mathrm{2}}{x}\right)\right)−\mathrm{1}}{{x}^{\alpha} } \\ $$

Question Number 111357    Answers: 0   Comments: 0

∫_0 ^1 ((tan^(−1) x)/(1+x^3 ))dx

$$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{tan}^{−\mathrm{1}} {x}}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 111351    Answers: 2   Comments: 0

(√(bemath)) lim_(x→−∞) ((x−(√(4x^2 +1)))/( (√(x^2 +2x+1)))) ?

$$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{x}−\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}}}\:? \\ $$

Question Number 111347    Answers: 0   Comments: 0

convert the plane with cartesian equation: x−3y + 2z = 7 into its vector parametric form.

$$\mathrm{convert}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{with}\:\mathrm{cartesian}\:\mathrm{equation}:\:{x}−\mathrm{3}{y}\:+\:\mathrm{2}{z}\:=\:\mathrm{7} \\ $$$$\:\mathrm{into}\:\mathrm{its}\:\mathrm{vector}\:\mathrm{parametric}\:\mathrm{form}. \\ $$$$ \\ $$

Question Number 111344    Answers: 0   Comments: 3

(√3)!=?

$$\sqrt{\mathrm{3}}!=? \\ $$

Question Number 111343    Answers: 0   Comments: 1

i!=?

$${i}!=? \\ $$

Question Number 111342    Answers: 1   Comments: 0

When the terms of a Geometric Progression(GP) with common ratio r=2 is added to the corresponding terms of an Arithmetic Provression (AP), a new sequence is formed. If the first terms of the GP and AP are the same and the first three terms of the new sequence are 3, 7 and 11 respectively, find the n^(th) term of the seauence.

$$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\left(\mathrm{GP}\right) \\ $$$$\mathrm{with}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{Arithmetic}\:\mathrm{Provression}\:\left(\mathrm{AP}\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{seauence}. \\ $$

Question Number 111340    Answers: 1   Comments: 2

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