Question and Answers Forum

AllQuestion and Answers: Page 1035

Question Number 116455 Answers: 0 Comments: 0

Question Number 116452 Answers: 2 Comments: 0

Question Number 116451 Answers: 3 Comments: 1

lim_(n→∞) ((((n+1)(n+2)(n+3)...(n+n)))^(1/n) /n) =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{n}}]{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}+\mathrm{3}\right)...\left(\mathrm{n}+\mathrm{n}\right)}}{\mathrm{n}}\:=? \\ $$

Question Number 116448 Answers: 2 Comments: 0

If sin (P) = −(8/(17)) ,where ((3π)/2)<P<2π and cos (Q)=−((24)/(25)), where π<Q<((3π)/2) what is the value of cos (2P+Q) =?

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{P}\right)\:=\:−\frac{\mathrm{8}}{\mathrm{17}}\:,\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\mathrm{P}<\mathrm{2}\pi \\ $$$$\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{24}}{\mathrm{25}},\:\mathrm{where}\:\pi<\mathrm{Q}<\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\left(\mathrm{2P}+\mathrm{Q}\right)\:=? \\ $$

Question Number 116443 Answers: 0 Comments: 0

Question Number 116441 Answers: 2 Comments: 0

If sin (45°−x) = −(1/3) , where 45°<x<90° .What is the value of (6sin x−(√2))^2

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\:,\:\mathrm{where}\:\mathrm{45}°<\mathrm{x}<\mathrm{90}° \\ $$$$.\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{6sin}\:\mathrm{x}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$

Question Number 116437 Answers: 2 Comments: 0

Prove that π<((22)/7)

$$\mathrm{Prove}\:\mathrm{that}\:\pi<\frac{\mathrm{22}}{\mathrm{7}} \\ $$

Question Number 116433 Answers: 2 Comments: 0

Given f(θ) = 2^(cos^2 (θ)) + 2^(sin^2 (θ)) find { ((maximum value)),((minimum value)) :}

$$\mathrm{Given}\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{2}^{\mathrm{cos}\:^{\mathrm{2}} \left(\theta\right)} \:+\:\mathrm{2}^{\mathrm{sin}\:^{\mathrm{2}} \left(\theta\right)} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{maximum}\:\mathrm{value}}\\{\mathrm{minimum}\:\mathrm{value}}\end{cases} \\ $$

Question Number 116427 Answers: 1 Comments: 0

∫ (sec x−tan x)^2 dx =?

$$\:\int\:\left(\mathrm{sec}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$

Question Number 116425 Answers: 2 Comments: 1

y′−y = −2xy^3

$$\:\mathrm{y}'−\mathrm{y}\:=\:−\mathrm{2xy}^{\mathrm{3}} \\ $$

Question Number 116418 Answers: 2 Comments: 0

∫ (dx/(x^5 (√(4+x^2 )))) =?

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{5}} \:\sqrt{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }}\:=? \\ $$

Question Number 116417 Answers: 2 Comments: 0

lim_(x→0) (((√(1+x sin x)) −(√(cos 2x)) )/(tan^2 ((x/2)))) =?

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

Question Number 116413 Answers: 0 Comments: 0

Question Number 116397 Answers: 2 Comments: 0

The number 1,2,3,4,...,7 are randomly divided into two non −empty subsets. The probability that the sum of the numbers in the two subsets being equal is (r/s) expressed in the lowest term. Find r+s ?

$${The}\:{number}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},...,\mathrm{7}\:{are}\:{randomly} \\ $$$${divided}\:{into}\:{two}\:{non}\:−{empty}\:{subsets}. \\ $$$${The}\:{probability}\:{that}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{in}\:{the}\:{two}\:{subsets}\:{being} \\ $$$${equal}\:{is}\:\frac{{r}}{{s}}\:{expressed}\:{in}\:{the}\:{lowest} \\ $$$${term}.\:{Find}\:{r}+{s}\:? \\ $$

Question Number 116436 Answers: 3 Comments: 2

... advanced calculus... evaluate :: I= ∫_( 0) ^( ∞) (((sin(x).sin(2x))/x)) dx =??? ... m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:{evaluate}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\:\mathrm{0}} ^{\:\:\infty} \:\:\left(\frac{{sin}\left({x}\right).{sin}\left(\mathrm{2}{x}\right)}{{x}}\right)\:{dx}\:=???\: \\ $$$$\:\:\:\:\:\:\:\:\:...\:{m}.{n}.\mathrm{1970}... \\ $$$$\: \\ $$$$ \\ $$

Question Number 116391 Answers: 1 Comments: 7

∫ (dx/((x+1)(√x) )) ?

$$\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}}\:}\:? \\ $$

Question Number 116385 Answers: 3 Comments: 0

∫ ((xe^x )/( (√(1+e^x )))) dx

$$\:\int\:\frac{\mathrm{xe}^{\mathrm{x}} }{\:\sqrt{\mathrm{1}+\mathrm{e}^{\mathrm{x}} }}\:\mathrm{dx}\: \\ $$

Question Number 116376 Answers: 2 Comments: 0

Let f be a function defined on non zero real numbers such that ((27 f(−x))/x) −x^2 f((1/x)) =−2x^2 for ∀x ≠ 0 . Find → { ((f(x))),((f(3))) :} ?

$$\mathrm{Let}\:\mathrm{f}\:\mathrm{be}\:\mathrm{a}\:\mathrm{function}\:\mathrm{defined}\:\mathrm{on}\:\mathrm{non}\:\mathrm{zero}\:\: \\ $$$$\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{27}\:\mathrm{f}\left(−\mathrm{x}\right)}{\mathrm{x}}\:−\mathrm{x}^{\mathrm{2}} \:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=−\mathrm{2x}^{\mathrm{2}} \\ $$$$\mathrm{for}\:\forall\mathrm{x}\:\neq\:\mathrm{0}\:.\:\mathrm{Find}\:\rightarrow\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)}\\{\mathrm{f}\left(\mathrm{3}\right)}\end{cases}\:?\: \\ $$

Question Number 116375 Answers: 2 Comments: 0

... nice calculus... ordinary differential equation(o.d.e) y(d^2 y/dx^2 ) −((dy/dx))^2 =y^2 (lny) ... find : general solution ..m.n.1970..

$$\:\:\:\:\:\:\:...\:\:{nice}\:\:{calculus}... \\ $$$$\:{ordinary}\:{differential} \\ $$$${equation}\left({o}.{d}.{e}\right) \\ $$$$\:\:\: \\ $$$$\:\:\:{y}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} ={y}^{\mathrm{2}} \left({lny}\right)\:\:... \\ $$$$\:\:\:{find}\::\:\:{general}\:\:{solution} \\ $$$$\:\:\:\:\:..{m}.{n}.\mathrm{1970}.. \\ $$

Question Number 116374 Answers: 2 Comments: 0

Determine the maximum value of ((1+cos x)/(sin x+cos x+2)) where x ranges over all real numbers.

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}+\mathrm{2}}\:\mathrm{where}\:\mathrm{x}\:\mathrm{ranges}\:\mathrm{over}\:\mathrm{all} \\ $$$$\mathrm{real}\:\mathrm{numbers}. \\ $$

Question Number 116367 Answers: 2 Comments: 0

Question Number 116365 Answers: 1 Comments: 0

Question Number 116363 Answers: 0 Comments: 0

Question Number 116361 Answers: 1 Comments: 1

Question Number 116360 Answers: 1 Comments: 0

A five digits number divisible by 3 is to be formed using the number 0,1,2,3,4 and 5 without repetition The total number of ways this can be done is __

$$\mathrm{A}\:\mathrm{five}\:\mathrm{digits}\:\mathrm{number}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3} \\ $$$$\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{and}\:\mathrm{5}\:\mathrm{without}\:\mathrm{repetition} \\ $$$$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{this}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{done}\:\mathrm{is}\:\_\_ \\ $$

Question Number 116359 Answers: 1 Comments: 0

If 0 < θ < (π/4) such that cosec θ−sec θ=((√(13))/6) then cot θ−tan θ equals to __

$$\mathrm{If}\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{4}}\:\mathrm{such}\:\mathrm{that}\:\mathrm{cosec}\:\theta−\mathrm{sec}\:\theta=\frac{\sqrt{\mathrm{13}}}{\mathrm{6}} \\ $$$$\mathrm{then}\:\mathrm{cot}\:\theta−\mathrm{tan}\:\theta\:\mathrm{equals}\:\mathrm{to}\:\_\_ \\ $$

Pg 1030 Pg 1031 Pg 1032 Pg 1033 Pg 1034 Pg 1035 Pg 1036 Pg 1037 Pg 1038 Pg 1039

Contact: info@tinkutara.com