Question and Answers Forum

AllQuestion and Answers: Page 1210

Question Number 87298 Answers: 1 Comments: 0

If y=sin x , x=0 to x=2π is revolved about the x-axis, find the surface of the solid of revolution.

$${If}\:{y}=\mathrm{sin}\:{x}\:,\:\:{x}=\mathrm{0}\:{to}\:{x}=\mathrm{2}\pi\:{is} \\ $$$${revolved}\:{about}\:{the}\:{x}-{axis},\:{find} \\ $$$${the}\:{surface}\:{of}\:{the}\:{solid}\:{of} \\ $$$${revolution}. \\ $$

Question Number 87296 Answers: 1 Comments: 0

If ellipse (x^2 /a^2 )+(y^2 /b^2 )=1 (a>b) is rotated about x-axis, find the surface of the solid of revolution.

$${If}\:\:{ellipse}\:\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}\:\:\left({a}>{b}\right) \\ $$$${is}\:{rotated}\:{about}\:{x}-{axis},\:{find}\:{the} \\ $$$${surface}\:{of}\:{the}\:{solid}\:{of}\:{revolution}. \\ $$

Question Number 87285 Answers: 1 Comments: 1

Question Number 87279 Answers: 3 Comments: 2

∫(x^2 /(1+x^4 ))dx

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

Question Number 87275 Answers: 1 Comments: 0

If the equations x^2 +ax+b=0 and x^2 +bx+a=0 have a common root, then the numerical value of a+b is

$$\mathrm{If}\:\:\mathrm{the}\:\mathrm{equations}\:{x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0}\:\mathrm{and}\: \\ $$$${x}^{\mathrm{2}} +{bx}+{a}=\mathrm{0}\:\mathrm{have}\:\mathrm{a}\:\mathrm{common}\:\mathrm{root}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value}\:\mathrm{of}\:{a}+{b}\:\mathrm{is} \\ $$

Question Number 87274 Answers: 0 Comments: 0

If the equations x^2 +ax+b=0 and x^2 +bx+a=0 have a common root, then the numerical value of a+b is

Question Number 87273 Answers: 0 Comments: 0

If the equations x^2 +ax+b=0 and x^2 +bx+a=0 have a common root, then the numerical value of a+b is

Question Number 87272 Answers: 1 Comments: 0

If the equations x^2 +ax+b=0 and x^2 +bx+a=0 have a common root, then the numerical value of a+b is

Question Number 87253 Answers: 1 Comments: 0

Three pair of socks are placed in a box.If two socks are drawn at random from the box What is the probability (a)of drawing a match pair (b)of drawing a socks for the left and right feet (c)of drawing two socks of the right feet d)drawing two socks of left feet (e)drawing socks of the same feet

$${Three}\:{pair}\:{of}\:{socks}\:{are} \\ $$$${placed}\:{in}\:{a}\:{box}.{If}\:{two} \\ $$$${socks}\:{are}\:{drawn}\:{at} \\ $$$${random}\:{from}\:{the}\:{box} \\ $$$${What}\:{is}\:{the}\:{probability} \\ $$$$\left({a}\right){of}\:{drawing}\:\:{a}\:{match} \\ $$$${pair} \\ $$$$\left({b}\right){of}\:{drawing}\:{a}\:{socks} \\ $$$${for}\:{the}\:{left}\:{and}\:{right} \\ $$$${feet} \\ $$$$\left({c}\right){of}\:{drawing}\:{two}\:{socks}\:{of} \\ $$$${the}\:{right}\:{feet} \\ $$$$\left.{d}\right){drawing}\:{two}\:{socks}\:{of} \\ $$$${left}\:{feet} \\ $$$$\left({e}\right){drawing}\:{socks}\:{of}\:{the} \\ $$$${same}\:{feet} \\ $$$$ \\ $$

Question Number 87250 Answers: 0 Comments: 0

((cos (π/7)))^(1/(3 )) + ((cos ((3π)/7)))^(1/(3 )) + ((cos ((5π)/7)))^(1/(3 )) =?

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\pi}{\mathrm{7}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{7}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{7}}}\:=? \\ $$$$ \\ $$

Question Number 87243 Answers: 1 Comments: 1

lim_(x→0) ((x− sin x)/(√((1−cos x)^p ))) = k k = constant , find p

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\:\mathrm{sin}\:{x}}{\sqrt{\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{{p}} }}\:=\:{k}\: \\ $$$${k}\:=\:{constant}\:,\:\mathrm{find}\:\mathrm{p}\: \\ $$

Question Number 87224 Answers: 1 Comments: 7

how to simply the boolean algebra (X+Y+Z)(X′ +Y+Z) (X+Y′+Z)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{simply}\:\mathrm{the}\: \\ $$$$\mathrm{boolean}\:\mathrm{algebra}\:\left(\mathrm{X}+\mathrm{Y}+\mathrm{Z}\right)\left(\mathrm{X}'\:+\mathrm{Y}+\mathrm{Z}\right) \\ $$$$\left(\mathrm{X}+\mathrm{Y}'+\mathrm{Z}\right)\: \\ $$

Question Number 87222 Answers: 0 Comments: 1

Question Number 87245 Answers: 0 Comments: 12

expand (1+x)^(−1) using maclaurins theorem and talyors formula

$${expand}\: \\ $$$$\left(\mathrm{1}+{x}\right)^{−\mathrm{1}} \\ $$$${using}\:{maclaurins} \\ $$$${theorem}\:{and}\:{talyors} \\ $$$${formula} \\ $$

Question Number 87194 Answers: 2 Comments: 6

find the solution of ((∣ log_2 (x)+2∣)/(x−3)) < 2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\frac{\mid\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{2}\mid}{\mathrm{x}−\mathrm{3}}\:<\:\mathrm{2}\: \\ $$

Question Number 87179 Answers: 0 Comments: 2

Question Number 87175 Answers: 1 Comments: 2

if in the expansion of (1+x)^n the coefficient of x^9 is the aritmetic mean of the coeficients of x^8 and x^(10) . find the possible value of n where n is a positive integer

$$\mathrm{if}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} \:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{9}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{aritmetic}\: \\ $$$$\mathrm{mean}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coeficients}\:\mathrm{of}\:\mathrm{x}^{\mathrm{8}} \:\mathrm{and}\: \\ $$$$\mathrm{x}^{\mathrm{10}} .\:\mathrm{find}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{value}\: \\ $$$$\mathrm{of}\:\mathrm{n}\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer} \\ $$

Question Number 87171 Answers: 0 Comments: 2

Given f(x) = 2 sin^2 x − sin x + 1 , 0 ≤ x ≤ 2π Find maximum and minumum value of f(x) without differential .

$${Given}\:\:{f}\left({x}\right)\:\:=\:\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{sin}\:{x}\:+\:\mathrm{1}\:\:,\:\:\mathrm{0}\:\:\leqslant\:{x}\:\leqslant\:\mathrm{2}\pi \\ $$$${Find}\:\:{maximum}\:\:{and}\:\:{minumum}\:\:{value} \\ $$$${of}\:\:{f}\left({x}\right)\:\:{without}\:\:{differential}\:. \\ $$

Question Number 87168 Answers: 0 Comments: 15

Calculate these limits: Please sirs detail

$${Calculate}\:{these}\:{limits}: \\ $$$${Please}\:{sirs}\:{detail}\: \\ $$

Question Number 87185 Answers: 3 Comments: 0

∫((2x−1)/(x(x^2 +3)))dx

$$\int\frac{\mathrm{2}{x}−\mathrm{1}}{{x}\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$

Question Number 87153 Answers: 1 Comments: 2

lim_(x→0) ((e^x +e^(−x) −2)/x^2 )