Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1612

Question Number 37817    Answers: 1   Comments: 1

calculate lim_(n→+∞) x^n (1−cos((π/x^n ))) with x from R and x≠0

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{x}^{{n}} \left(\mathrm{1}−{cos}\left(\frac{\pi}{{x}^{{n}} }\right)\right)\:{with}\:{x} \\ $$$${from}\:{R}\:{and}\:{x}\neq\mathrm{0} \\ $$

Question Number 37816    Answers: 0   Comments: 1

find lim_(x→0) ((ln(x+e^(sinx) ) −x^2 )/(sh(2x)))

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{ln}\left({x}+{e}^{{sinx}} \right)\:−{x}^{\mathrm{2}} }{{sh}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 37815    Answers: 1   Comments: 1

let I = ∫_0 ^∞ e^(−x) cos^2 (π[x])dx and J = ∫_0 ^∞ e^(−x) sin^2 (π[x])dx 1) calculate I +J and I −J 2) find the values of I and J.

$${let}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{cos}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{sin}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:\:{and}\:{I}\:−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:{I}\:{and}\:{J}. \\ $$

Question Number 37813    Answers: 1   Comments: 0

find A_n = ∫_(1/n) ^1 x(√x)arctan(x+(1/x))dx then calculate lim_(n→+∞) A_n .

$${find}\:{A}_{{n}} \:\:=\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\:{x}\sqrt{{x}}{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$$${then}\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} . \\ $$

Question Number 37812    Answers: 1   Comments: 1

calculate ∫_0 ^∞ e^(−2x) sin{π[x]}dx .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{x}} {sin}\left\{\pi\left[{x}\right]\right\}{dx}\:. \\ $$

Question Number 37804    Answers: 2   Comments: 1

Question Number 37796    Answers: 0   Comments: 0

Find (dy/dx) if y= (x^2 + 1)^2 and y= (1−3x^2 )^5

$${Find}\:\frac{{dy}}{{dx}}\:{if}\: \\ $$$${y}=\:\left({x}^{\mathrm{2}} +\:\mathrm{1}\right)^{\mathrm{2}} \\ $$$${and}\:{y}=\:\left(\mathrm{1}−\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{5}} \\ $$

Question Number 37795    Answers: 1   Comments: 0

The side of a square is increasing at a rate of 0.1cms^(−1) . Find the rate of increase of the perimeter of the square when the length of side is 4cm.

$${The}\:{side}\:{of}\:{a}\:{square}\:{is}\:{increasing} \\ $$$${at}\:{a}\:{rate}\:{of}\:\mathrm{0}.\mathrm{1}{cms}^{−\mathrm{1}} .\:{Find}\:{the} \\ $$$${rate}\:{of}\:{increase}\:{of}\:{the}\:{perimeter} \\ $$$${of}\:{the}\:{square}\:{when}\:{the}\:{length}\:{of} \\ $$$${side}\:{is}\:\mathrm{4}{cm}. \\ $$

Question Number 37784    Answers: 2   Comments: 1

find ∫_0 ^(π/4) (dx/(2cosx +cos(2x)))

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$

Question Number 37777    Answers: 2   Comments: 0

Find the shortest distance between the curves 9x^2 +9y^2 −30y+16=0 and y^2 =x^3 .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{curves}\:\mathrm{9}{x}^{\mathrm{2}} +\mathrm{9}{y}^{\mathrm{2}} −\mathrm{30}{y}+\mathrm{16}=\mathrm{0}\:{and} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{3}} \:. \\ $$

Question Number 37768    Answers: 0   Comments: 4

quest for truth...then study the books...

$${quest}\:{for}\:{truth}...{then}\:{study}\:{the}\:{books}... \\ $$

Question Number 37755    Answers: 0   Comments: 1

Question Number 37754    Answers: 0   Comments: 0

Question Number 37751    Answers: 2   Comments: 8

Question Number 37750    Answers: 0   Comments: 1

Given the angle x, construct the angle y if (1) sin y = 2 sin x (2) tan y = 3 tan x (3) cos y = (1/2)cos x (4) sec y = cosec x hey do not construct it just find it out the ∠y for the every given cases

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{angle}\:{x},\:\mathrm{construct}\:\mathrm{the}\:\mathrm{angle}\:{y}\:\mathrm{if}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}\:{y}\:=\:\mathrm{2}\:\mathrm{sin}\:{x} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{tan}\:{y}\:=\:\mathrm{3}\:\mathrm{tan}\:{x} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{cos}\:{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:{x}\: \\ $$$$\left(\mathrm{4}\right)\:\mathrm{sec}\:{y}\:=\:\mathrm{cosec}\:{x} \\ $$$$\mathrm{hey}\:\mathrm{do}\:\mathrm{not}\:\mathrm{construct}\:\mathrm{it}\:\mathrm{just}\:\mathrm{find}\:\mathrm{it}\:\mathrm{out}\:\mathrm{the}\:\angle{y}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{every}\:\mathrm{given}\:\mathrm{cases} \\ $$

Question Number 37745    Answers: 1   Comments: 0

Show that the equation sec^2 θ = ((4xy)/((x+y)^2 )) is only possible when x = y

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{sec}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{xy}}{\left({x}+{y}\right)^{\mathrm{2}} }\:\mathrm{is}\: \\ $$$$\mathrm{only}\:\mathrm{possible}\:\mathrm{when}\:{x}\:=\:{y} \\ $$

Question Number 37738    Answers: 0   Comments: 4

given a^2 <1 now a<(√1) or a<±1 ∴ a<1 and a<−1 but but its false we know if a^2 <1 so −1<a<1 so my question is why this is happening at all.

$$\mathrm{given}\:{a}^{\mathrm{2}} <\mathrm{1} \\ $$$$\mathrm{now} \\ $$$${a}<\sqrt{\mathrm{1}} \\ $$$$\mathrm{or}\:{a}<\pm\mathrm{1} \\ $$$$\therefore\:{a}<\mathrm{1}\:\mathrm{and}\:{a}<−\mathrm{1}\:\:\:\:\mathrm{but}\:\mathrm{but}\:\mathrm{its}\:\mathrm{false}\:\mathrm{we}\:\mathrm{know} \\ $$$${if}\:\mathrm{a}^{\mathrm{2}} <\mathrm{1}\:\mathrm{so}\:−\mathrm{1}<{a}<\mathrm{1}\: \\ $$$${so}\:{my}\:{question}\:{is}\:{why}\:{this}\:{is}\:{happening}\:{at}\:{all}. \\ $$

Question Number 37733    Answers: 1   Comments: 0

Prove that the equation sin θ = x + (1/x) is impossible if x be real.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{sin}\:\theta\:=\:{x}\:+\:\frac{\mathrm{1}}{{x}}\: \\ $$$$\mathrm{is}\:\mathrm{impossible}\:\mathrm{if}\:{x}\:\mathrm{be}\:\mathrm{real}. \\ $$

Question Number 37730    Answers: 1   Comments: 1

Differentiate x(1+x)^4

$$\:{Differentiate}\: \\ $$$${x}\left(\mathrm{1}+{x}\right)^{\mathrm{4}} \: \\ $$$$ \\ $$

Question Number 37728    Answers: 1   Comments: 0

1+n+((n(n−1))/(2!))+((n(n−1)(n−2))/(3!))+((n(n−1)(n−2)(n−3))/(4!))+........=

$$\mathrm{1}+\mathrm{n}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)}{\mathrm{2}!}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)}{\mathrm{3}!}+\frac{\mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)\left(\mathrm{n}−\mathrm{3}\right)}{\mathrm{4}!}+........= \\ $$

Question Number 37712    Answers: 1   Comments: 1

Evaluate Σ_(r=0) ^∞ 2^(r−1)

$${Evaluate}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{2}^{{r}−\mathrm{1}} \\ $$

Question Number 37711    Answers: 1   Comments: 0

A commitee of 2 boys and 1 girl has to be formed from a class of 4 boys and 3 girls give the number of ways these can be done

$${A}\:{commitee}\:{of}\:\mathrm{2}\:{boys}\:{and}\:\mathrm{1}\:{girl} \\ $$$${has}\:{to}\:{be}\:{formed}\:{from}\:{a}\:{class} \\ $$$${of}\:\mathrm{4}\:{boys}\:{and}\:\mathrm{3}\:{girls}\:{give}\:{the}\:{number} \\ $$$${of}\:{ways}\:{these}\:{can}\:{be}\:{done} \\ $$

Question Number 37692    Answers: 2   Comments: 0

2+6+12+20+30+42+.........+n=(1/3)(n)(n−1)(n−2) is this true. if yes so please derive it from L.H.S hey I just noticed I got 15yrs and 5 months older

$$\mathrm{2}+\mathrm{6}+\mathrm{12}+\mathrm{20}+\mathrm{30}+\mathrm{42}+.........+\mathrm{n}=\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{n}\right)\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right) \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{true}.\:\mathrm{if}\:\mathrm{yes}\:\mathrm{so}\:\mathrm{please}\:\mathrm{derive}\:\mathrm{it}\:\mathrm{from}\:\mathrm{L}.\mathrm{H}.\mathrm{S} \\ $$$$\mathrm{hey}\:\mathrm{I}\:\mathrm{just}\:\mathrm{noticed}\:\mathrm{I}\:\mathrm{got}\:\mathrm{15yrs}\:\mathrm{and}\:\:\mathrm{5}\:\mathrm{months}\:\mathrm{older} \\ $$

Question Number 37691    Answers: 0   Comments: 2

Sir Aifour, I just answered your question number 37209... greetings from a rainy Saturday evening in Vienna, Austria!

$$\mathrm{Sir}\:\mathrm{Aifour},\:\mathrm{I}\:\mathrm{just}\:\mathrm{answered}\:\mathrm{your}\:\mathrm{question} \\ $$$$\mathrm{number}\:\mathrm{37209}...\:\mathrm{greetings}\:\mathrm{from}\:\mathrm{a}\:\mathrm{rainy} \\ $$$$\mathrm{Saturday}\:\mathrm{evening}\:\mathrm{in}\:\mathrm{Vienna},\:\mathrm{Austria}! \\ $$

Question Number 37664    Answers: 1   Comments: 0

find ∫(1 + sinx)dx

$$\mathrm{find}\:\int\left(\mathrm{1}\:+\:{sinx}\right){dx} \\ $$

Question Number 37663    Answers: 3   Comments: 0

show that ((sin2A)/(1+cos2A)) = tanA.

$$\mathrm{show}\:\mathrm{that}\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+{cos}\mathrm{2}{A}}\:=\:\mathrm{tanA}. \\ $$

  Pg 1607      Pg 1608      Pg 1609      Pg 1610      Pg 1611      Pg 1612      Pg 1613      Pg 1614      Pg 1615      Pg 1616   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com