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Question Number 111447 Answers: 1 Comments: 1

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.

Pg 1001 Pg 1002 Pg 1003 Pg 1004 Pg 1005 Pg 1006 Pg 1007 Pg 1008 Pg 1009 Pg 1010

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