Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1082

Question Number 107036 Answers: 2 Comments: 1

∫ (((√(1+x^2 )) dx)/x^4 ) ?

$$\int\:\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} }\:? \\ $$

Question Number 107033 Answers: 0 Comments: 0

Question Number 107030 Answers: 4 Comments: 1

lim_(x→0) (2+(3/x))^(1/(4x−2))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{2}+\frac{\mathrm{3}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \\ $$

Question Number 107028 Answers: 3 Comments: 1

@bemath@ lim_(x→∞) (2+3x)^(1/(4x−2))

$$\:\:\:@{bemath}@ \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}+\mathrm{3}{x}\right)^{\frac{\mathrm{1}}{\mathrm{4}{x}−\mathrm{2}}} \\ $$

Question Number 107018 Answers: 1 Comments: 2

Given f(x)=((10)/(2−sin 2x)). Find maximum value f(x).

$$\mathcal{G}{iven}\:{f}\left({x}\right)=\frac{\mathrm{10}}{\mathrm{2}−\mathrm{sin}\:\mathrm{2}{x}}.\:{Find}\:{maximum}\:{value}\: \\ $$$${f}\left({x}\right). \\ $$

Question Number 107034 Answers: 0 Comments: 6

Question Number 107002 Answers: 3 Comments: 0

∫_0 ^π ((cosx)/(√(2−sin^2 x)))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cosx}}{\sqrt{\mathrm{2}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}}}\mathrm{dx} \\ $$

Question Number 106997 Answers: 0 Comments: 3

Question Number 106990 Answers: 1 Comments: 4

Two places A and B both on a parallel of latitude α°N differs in longitudes by θ°. Show that the shortest distance between them is: (([2 sin^(− 1) (cos α sin (θ/2))])/(360)) × 2πR Topic: Longitude and Latitude

$$\mathrm{Two}\:\mathrm{places}\:\:\mathrm{A}\:\:\mathrm{and}\:\:\mathrm{B}\:\:\mathrm{both}\:\mathrm{on}\:\mathrm{a}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\:\alpha°\mathrm{N} \\ $$$$\mathrm{differs}\:\mathrm{in}\:\mathrm{longitudes}\:\mathrm{by}\:\:\theta°.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance} \\ $$$$\mathrm{between}\:\mathrm{them}\:\mathrm{is}:\:\:\:\:\:\frac{\left[\mathrm{2}\:\mathrm{sin}^{−\:\mathrm{1}} \left(\mathrm{cos}\:\alpha\:\mathrm{sin}\:\frac{\theta}{\mathrm{2}}\right)\right]}{\mathrm{360}}\:\:×\:\:\mathrm{2}\pi\mathrm{R} \\ $$$$ \\ $$$$\mathrm{Topic}:\:\:\mathrm{Longitude}\:\mathrm{and}\:\mathrm{Latitude} \\ $$

Question Number 106983 Answers: 2 Comments: 0

Question Number 106977 Answers: 3 Comments: 0

Question Number 106964 Answers: 5 Comments: 4

∫_0 ^π ((sec^2 x)/(√(1−tan^2 x)))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}}{\sqrt{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \mathrm{x}}}\mathrm{dx} \\ $$

Question Number 106958 Answers: 2 Comments: 0

@bemath@ (1) Given { ((x=sin α+sin β)),((y=cos α+cos β)) :} maximum value of x^2 +y^2 when α=... (2) find solution set the equation sin^4 x + sin^4 (x+(π/4))=(1/4) where x ∈ [0,2π]

$$\:\:\:@{bemath}@ \\ $$$$\left(\mathrm{1}\right)\:{Given}\:\begin{cases}{{x}=\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta}\\{{y}=\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}\end{cases} \\ $$$${maximum}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{when}\:\alpha=... \\ $$$$\left(\mathrm{2}\right)\:{find}\:{solution}\:{set}\:{the}\:{equation} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} {x}\:+\:\mathrm{sin}\:^{\mathrm{4}} \left({x}+\frac{\pi}{\mathrm{4}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\:{where}\:{x}\:\in\:\left[\mathrm{0},\mathrm{2}\pi\right]\: \\ $$

Question Number 106956 Answers: 3 Comments: 0

Question Number 106996 Answers: 1 Comments: 1

@bemath@ log _(∣2x−(1/2)∣) (x+1+(1/x))≥log _(∣2x−(1/2)∣) (x^2 +1+(1/x^2 ))

$$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}+\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right) \\ $$

Question Number 106948 Answers: 4 Comments: 0

let f(a) =∫_0 ^π (dx/(a+cos^2 x)) with a>0 1) explicite f(a) 2)explicite g(a) =∫_0 ^π (dx/((a+cos^2 x)^2 )) 3) find tbe valued of intevrsls ∫_0 ^π (dx/(1+cos^2 x)) and ∫_0 ^π (dx/((1+cos^2 x)^2 ))

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\:\mathrm{with}\:\mathrm{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{explicite}\:\mathrm{f}\left(\mathrm{a}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{\mathrm{dx}}{\left(\mathrm{a}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{tbe}\:\mathrm{valued}\:\mathrm{of}\:\mathrm{intevrsls} \\ $$$$\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}\right)^{\mathrm{2}} } \\ $$

Question Number 107051 Answers: 2 Comments: 0

∫_0 ^π ((cosx)/(2+sin^2 x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cosx}}{\mathrm{2}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$

Question Number 106941 Answers: 1 Comments: 0

Find the maximum value of Σ_(i=1) ^n sin^5 θ_i with Σ_(i=1) ^n sin θ_i =0.

$${Find}\:{the}\:{maximum}\:{value}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}^{\mathrm{5}} \:\theta_{{i}} \\ $$$${with}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\:\theta_{{i}} =\mathrm{0}. \\ $$

Question Number 106938 Answers: 0 Comments: 0

Question Number 106932 Answers: 3 Comments: 0

∫_0 ^π (x/(1+cos^2 x))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$

Question Number 106928 Answers: 1 Comments: 0

Imagine a planet having a mass twice that of the earth and a radius equal to 1.414 times that of the earth. Determine the acceleration due to gravity at its surface.

$${Imagine}\:{a}\:{planet}\:{having}\:{a}\:{mass}\:{twice}\:{that} \\ $$$${of}\:{the}\:{earth}\:{and}\:{a}\:{radius}\:{equal}\:{to}\:\mathrm{1}.\mathrm{414} \\ $$$${times}\:{that}\:{of}\:{the}\:{earth}.\:{Determine}\:{the} \\ $$$${acceleration}\:{due}\:{to}\:{gravity}\:{at}\:{its}\:{surface}. \\ $$

Question Number 106943 Answers: 3 Comments: 1

Question Number 106950 Answers: 1 Comments: 0

^(@bemath@) Given { ((2cos x+7cos y =5)),((2sin x+7sin y = 6)) :} cos (x−y) =?

$$\:\:\:\:\:\:\:\:\:\:^{@{bemath}@} \\ $$$${Given}\:\begin{cases}{\mathrm{2cos}\:{x}+\mathrm{7cos}\:{y}\:=\mathrm{5}}\\{\mathrm{2sin}\:{x}+\mathrm{7sin}\:{y}\:=\:\mathrm{6}}\end{cases} \\ $$$$\mathrm{cos}\:\left({x}−{y}\right)\:=?\: \\ $$

Question Number 106921 Answers: 1 Comments: 1

Question Number 106919 Answers: 0 Comments: 2

if the wheel of a car moved 56rev. what is the distance the car moved in 14s?

$$\mathrm{if}\:\mathrm{the}\:\mathrm{wheel}\:\mathrm{of}\:\mathrm{a}\:\mathrm{car}\:\mathrm{moved}\:\mathrm{56rev}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{the}\:\mathrm{car}\:\mathrm{moved}\:\mathrm{in}\:\mathrm{14s}? \\ $$

Question Number 106944 Answers: 1 Comments: 2

If Σ_(i= 1) ^n sin (θ_i ) = n then cos (θ_1 ) + cos (θ_2 ) + cos (θ_3 ) + ... + cos (θ_n ) = ? i got 0 as answer. please who can correct?

$$\mathrm{If}\:\underset{{i}=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{sin}\:\left(\theta_{{i}} \right)\:=\:{n}\:\mathrm{then}\:\:\mathrm{cos}\:\left(\theta_{\mathrm{1}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{2}} \right)\:+\:\mathrm{cos}\:\left(\theta_{\mathrm{3}} \right)\:+\:...\:+\:\mathrm{cos}\:\left(\theta_{{n}} \right)\:=\:? \\ $$$$\mathrm{i}\:\mathrm{got}\:\mathrm{0}\:\mathrm{as}\:\mathrm{answer}.\:\mathrm{please}\:\mathrm{who}\:\mathrm{can}\:\mathrm{correct}? \\ $$

Pg 1077 Pg 1078 Pg 1079 Pg 1080 Pg 1081 Pg 1082 Pg 1083 Pg 1084 Pg 1085 Pg 1086

Contact: info@tinkutara.com