Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1408

Question Number 63934    Answers: 1   Comments: 1

The coefficient of x^5 in the expansion of (2−x+3x^2 )^6 is

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\:{x}^{\mathrm{5}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{2}−{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{6}} \:\:\mathrm{is} \\ $$

Question Number 63930    Answers: 0   Comments: 0

Question Number 63927    Answers: 0   Comments: 7

∫_0 ^π (dx/((3+2cos x)^2 ))

$$\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{\left(\mathrm{3}+\mathrm{2}{cos}\:{x}\right)^{\mathrm{2}} } \\ $$

Question Number 63922    Answers: 0   Comments: 4

if f(x)= { (((log (1+2ax)−log (1−bx))/x),(x≠0)),(k,(x=0)) :} is continuous at x=0 then k=?

$$\mathrm{if}\:{f}\left({x}\right)=\begin{cases}{\frac{\mathrm{log}\:\left(\mathrm{1}+\mathrm{2}{ax}\right)−\mathrm{log}\:\left(\mathrm{1}−{bx}\right)}{{x}}}&{{x}\neq\mathrm{0}}\\{{k}}&{{x}=\mathrm{0}}\end{cases} \\ $$$$\mathrm{is}\:\mathrm{continuous}\:\mathrm{at}\:{x}=\mathrm{0}\:\mathrm{then}\:{k}=? \\ $$

Question Number 63921    Answers: 0   Comments: 2

lim_(n→∞) (((n/(n+1)))^α +sin (1/n))^n where α∈Q is equal to

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\left(\frac{{n}}{{n}+\mathrm{1}}\right)^{\alpha} +\mathrm{sin}\:\frac{\mathrm{1}}{{n}}\right)^{{n}} \mathrm{where}\:\alpha\in\mathbb{Q} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 63920    Answers: 0   Comments: 5

If α,β are root of quadratic equation ax^2 +bx+c then lim_(x→α) ((1−cos (ax^2 +bx+c))/((x−α)^2 ))=?

$$\mathrm{If}\:\alpha,\beta\:\mathrm{are}\:\mathrm{root}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}\:\mathrm{then} \\ $$$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left({ax}^{\mathrm{2}} +{bx}+{c}\right)}{\left({x}−\alpha\right)^{\mathrm{2}} }=? \\ $$

Question Number 63919    Answers: 0   Comments: 3

Π_(n=2) ^∞ (1−(1/n^2 ))=?

$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 63918    Answers: 1   Comments: 0

lim_(x→π/2) (([1−tan x/2][1−sin x])/([1+tan x/2][π−2x]^3 ))=?

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\frac{\left[\mathrm{1}−\mathrm{tan}\:{x}/\mathrm{2}\right]\left[\mathrm{1}−\mathrm{sin}\:{x}\right]}{\left[\mathrm{1}+\mathrm{tan}\:{x}/\mathrm{2}\right]\left[\pi−\mathrm{2}{x}\right]^{\mathrm{3}} }=? \\ $$

Question Number 63917    Answers: 0   Comments: 2

lim_(x→∞) ((√(x+(√(x+(√x)))))−(√x))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}−\sqrt{{x}}\right) \\ $$

Question Number 63915    Answers: 0   Comments: 0

If p is nearly equal to q and n > 1, such that (((n+1)p+(n−1)q)/((n−1)p+(n+1)q)) = ((p/q))^k , then the value of k is

$$\mathrm{If}\:{p}\:\mathrm{is}\:\mathrm{nearly}\:\mathrm{equal}\:\:\mathrm{to}\:{q}\:\:\mathrm{and}\:\:{n}\:>\:\mathrm{1},\:\mathrm{such} \\ $$$$\mathrm{that}\:\frac{\left({n}+\mathrm{1}\right){p}+\left({n}−\mathrm{1}\right){q}}{\left({n}−\mathrm{1}\right){p}+\left({n}+\mathrm{1}\right){q}}\:=\:\left(\frac{{p}}{{q}}\right)^{{k}} ,\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is} \\ $$

Question Number 63909    Answers: 1   Comments: 1

The integral part of (8 + 3(√7) )^(20) is even.

$$\mathrm{The}\:\mathrm{integral}\:\mathrm{part}\:\mathrm{of}\:\left(\mathrm{8}\:+\:\mathrm{3}\sqrt{\mathrm{7}}\:\right)^{\mathrm{20}} \:\mathrm{is}\:\mathrm{even}. \\ $$

Question Number 63908    Answers: 0   Comments: 1

If R=(5(√5) +11)^(2n+1) = [R]+ F, where [R] denotes the greatest integer in R, then RF= 2^(2n+1) .

$$\mathrm{If}\:{R}=\left(\mathrm{5}\sqrt{\mathrm{5}}\:+\mathrm{11}\right)^{\mathrm{2}{n}+\mathrm{1}} =\:\left[{R}\right]+\:{F},\:\mathrm{where} \\ $$$$\left[{R}\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{in}\:{R},\: \\ $$$$\mathrm{then}\:{RF}=\:\mathrm{2}^{\mathrm{2}{n}+\mathrm{1}} . \\ $$

Question Number 63907    Answers: 1   Comments: 1

The coefficient of x^5 in (1+2x+3x^2 +...)^(−3/2) is 21.

$$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{in}\:\left(\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +...\right)^{−\mathrm{3}/\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{21}. \\ $$

Question Number 63904    Answers: 0   Comments: 1

Question Number 63903    Answers: 0   Comments: 0

Question Number 63900    Answers: 0   Comments: 1

Question Number 63895    Answers: 0   Comments: 0

Question Number 63894    Answers: 0   Comments: 1

sove the (de) x^2 y^′ −(2x+3)y =sin(x^2 ) with y(1)=2 and y^′ (1)=1 .

$${sove}\:{the}\:\left({de}\right)\:{x}^{\mathrm{2}} {y}^{'} \:−\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={sin}\left({x}^{\mathrm{2}} \right)\:\:{with}\:{y}\left(\mathrm{1}\right)=\mathrm{2}\:{and} \\ $$$${y}^{'} \left(\mathrm{1}\right)=\mathrm{1}\:. \\ $$

Question Number 63893    Answers: 0   Comments: 1

1) simplify W_n (z)=(1+z)(1+z^2 )....(1+z^2^n ) (z from C) 2) simplify P_n (θ) =(1+e^(iθ) )(1+e^(2iθ) ).....(1+e^(i2^n θ) ) and sove P_n (θ)=0

$$\left.\mathrm{1}\right)\:{simplify}\:{W}_{{n}} \left({z}\right)=\left(\mathrm{1}+{z}\right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)....\left(\mathrm{1}+{z}^{\mathrm{2}^{{n}} } \right)\:\left({z}\:{from}\:{C}\right) \\ $$$$\left.\mathrm{2}\right)\:{simplify}\:{P}_{{n}} \left(\theta\right)\:=\left(\mathrm{1}+{e}^{{i}\theta} \right)\left(\mathrm{1}+{e}^{\mathrm{2}{i}\theta} \right).....\left(\mathrm{1}+{e}^{{i}\mathrm{2}^{{n}} \theta} \right)\:{and}\:{sove} \\ $$$${P}_{{n}} \left(\theta\right)=\mathrm{0} \\ $$

Question Number 63892    Answers: 0   Comments: 3

calculate A=∫_0 ^∞ (x^(2017) /(1+x^(2019) )) dx and B =∫_0 ^∞ (x^(2019) /(1+x^(2021) )) dx calculate the fraction (A/B)

$${calculate}\:{A}=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2017}} }{\mathrm{1}+{x}^{\mathrm{2019}} }\:{dx}\:\:{and}\:{B}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{\mathrm{2019}} }{\mathrm{1}+{x}^{\mathrm{2021}} }\:{dx} \\ $$$${calculate}\:{the}\:{fraction}\:\frac{{A}}{{B}} \\ $$

Question Number 63891    Answers: 0   Comments: 0

A bus is travelling along a straight road at 100Km/hr and the bus conductor walks at 6Km/hr on the floor of the bus and in the same direction as the bus. Find the speed of the conductor relative to the road, and relative to the bus. If the bus conductor now works at the same rate but in the opposite direction as the bus, find his new speed relative to the road. Answers in textbook: 106Km/hr, 64Km/hr, 94Km/hr

$$\mathrm{A}\:\mathrm{bus}\:\mathrm{is}\:\mathrm{travelling}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{road}\:\mathrm{at}\:\mathrm{100Km}/\mathrm{hr}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{bus}\:\mathrm{conductor}\:\mathrm{walks}\:\mathrm{at}\:\mathrm{6Km}/\mathrm{hr}\:\mathrm{on}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bus} \\ $$$$\mathrm{and}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same}\:\mathrm{direction}\:\mathrm{as}\:\mathrm{the}\:\mathrm{bus}.\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{conductor}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the}\:\mathrm{road},\:\mathrm{and} \\ $$$$\mathrm{relative}\:\mathrm{to}\:\mathrm{the}\:\mathrm{bus}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{bus}\:\mathrm{conductor}\:\mathrm{now}\:\mathrm{works}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{rate}\:\mathrm{but}\:\mathrm{in}\:\mathrm{the}\:\mathrm{opposite}\:\mathrm{direction}\:\mathrm{as}\:\mathrm{the}\:\mathrm{bus},\:\mathrm{find}\:\mathrm{his}\:\mathrm{new}\:\mathrm{speed} \\ $$$$\mathrm{relative}\:\mathrm{to}\:\mathrm{the}\:\mathrm{road}. \\ $$$$\mathrm{Answers}\:\mathrm{in}\:\mathrm{textbook}:\:\:\:\:\mathrm{106Km}/\mathrm{hr},\:\:\:\:\mathrm{64Km}/\mathrm{hr},\:\:\:\:\:\mathrm{94Km}/\mathrm{hr} \\ $$

Question Number 63888    Answers: 2   Comments: 0

y = log_2 [log_3 (log_5 x)] y = ?

$${y}\:=\:{log}_{\mathrm{2}} \left[{log}_{\mathrm{3}} \left({log}_{\mathrm{5}} {x}\right)\right] \\ $$$${y}\:=\:? \\ $$

Question Number 63881    Answers: 0   Comments: 1

∫e^x /Lnxdx

$$\int{e}^{{x}} /{Lnxdx} \\ $$

Question Number 63883    Answers: 0   Comments: 1

∫ln(x)ln(1−x)ln(1−2x)dx

$$\int{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−\mathrm{2}{x}\right){dx} \\ $$

Question Number 63865    Answers: 0   Comments: 2

If ∫ ((4 e^x + 6 e^(−x) )/(9 e^x − 4 e^(−x) ))dx=Ax+B log(9e^(2x) −4)+C, then

$$\mathrm{If}\:\int\:\:\frac{\mathrm{4}\:{e}^{{x}} +\:\mathrm{6}\:{e}^{−{x}} }{\mathrm{9}\:{e}^{{x}} −\:\mathrm{4}\:{e}^{−{x}} }{dx}={Ax}+{B}\:\mathrm{log}\left(\mathrm{9}{e}^{\mathrm{2}{x}} −\mathrm{4}\right)+{C}, \\ $$$$\mathrm{then} \\ $$

Question Number 63862    Answers: 0   Comments: 2

If the 3rd term in the expansion of [x+x^(log_(10) x) ]^5 is 10^6 , then x may be

$$\mathrm{If}\:\mathrm{the}\:\mathrm{3rd}\:\mathrm{term}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left[{x}+{x}^{\mathrm{log}_{\mathrm{10}} {x}} \right]^{\mathrm{5}} \mathrm{is}\:\mathrm{10}^{\mathrm{6}} ,\:\mathrm{then}\:{x}\:\mathrm{may}\:\mathrm{be} \\ $$

  Pg 1403      Pg 1404      Pg 1405      Pg 1406      Pg 1407      Pg 1408      Pg 1409      Pg 1410      Pg 1411      Pg 1412   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com