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AllQuestion and Answers: Page 1881

Question Number 20882 Answers: 1 Comments: 0

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Question Number 20873 Answers: 1 Comments: 0

∫_1 ^5 (e^x /x^2 ) dx

$$\int_{\mathrm{1}} ^{\mathrm{5}} \frac{{e}^{{x}} }{{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 20872 Answers: 1 Comments: 0

if y=[xtan^(−1) x]−[(1/2)ln(1+x^2 )] show that (1+x^2 )y^(′′) =1

$${if}\:\:{y}=\left[{xtan}^{−\mathrm{1}} {x}\right]−\left[\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right] \\ $$$${show}\:{that}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} =\mathrm{1} \\ $$

Question Number 20871 Answers: 1 Comments: 0

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C×(A+B)=C×A+C×B prove it.

$$\boldsymbol{{C}}×\left(\boldsymbol{{A}}+\boldsymbol{{B}}\right)=\boldsymbol{{C}}×\boldsymbol{{A}}+\boldsymbol{{C}}×\boldsymbol{{B}}\: \\ $$$${prove}\:{it}. \\ $$

Question Number 20857 Answers: 0 Comments: 0

∫ (√(sin x)) + (√(cos x)) dx

$$\int\:\sqrt{\mathrm{sin}\:{x}}\:+\:\sqrt{\mathrm{cos}\:{x}}\:{dx} \\ $$

Question Number 20853 Answers: 0 Comments: 0

$$ \\ $$

Question Number 20851 Answers: 2 Comments: 0

if (x+y)^(m+n) =x^m y^n ,show that (dy/dx)=(y/x)

$${if}\:\left({x}+{y}\right)^{{m}+{n}} ={x}^{{m}} {y}^{{n}} ,{show}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$

Question Number 20850 Answers: 1 Comments: 0

given that y=log(√((1+cos^2 x)/(1−e^(2x) ))),find (dy/dx)

$${given}\:{that}\:{y}={log}\sqrt{\frac{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{\mathrm{1}−{e}^{\mathrm{2}{x}} }},{find} \\ $$$$\frac{{dy}}{{dx}} \\ $$

Question Number 20849 Answers: 1 Comments: 0

The time period,T of pendulum of length l is given by T=2Π(√(l/g))where l amd g are constant.Find the approximate percentage increase in time T, when the length of pendulum increases by 4%

$${The}\:{time}\:{period},{T}\:\:{of}\:{pendulum}\:{of} \\ $$$${length}\:{l}\:{is}\:{given}\:{by}\:{T}=\mathrm{2}\Pi\sqrt{\frac{{l}}{{g}}}{where} \\ $$$$\:{l}\:{amd}\:{g}\:{are}\:{constant}.{Find}\:{the}\: \\ $$$${approximate}\:{percentage}\:{increase}\: \\ $$$${in}\:{time}\:{T},\:{when}\:{the}\:{length}\:{of}\: \\ $$$${pendulum}\:{increases}\:{by}\:\mathrm{4\%} \\ $$

Question Number 20847 Answers: 1 Comments: 0

the rectangle is known to be twice as long as its wide.if the width is measured as 20 ±0.2cm. find the area in the form of (A±b)

$${the}\:{rectangle}\:{is}\:{known}\:{to}\:{be}\:{twice} \\ $$$${as}\:{long}\:{as}\:{its}\:{wide}.{if}\:{the}\:{width}\:{is} \\ $$$${measured}\:{as}\:\mathrm{20}\:\pm\mathrm{0}.\mathrm{2}{cm}. \\ $$$${find}\:{the}\:{area}\:{in}\:{the}\:{form}\:{of}\:\left({A}\pm{b}\right) \\ $$$$ \\ $$

Question Number 20867 Answers: 1 Comments: 0

The number of irrational roots of the equation (x − 1)(x − 2)(3x − 2)(3x + 1) = 21 is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{irrational}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{21}\:\mathrm{is} \\ $$

Question Number 20842 Answers: 1 Comments: 0

Acceleration of a particle which is at rest at x = 0 is a^→ = (4 − 2x) i^∧ . Select the correct alternative(s). (a) Maximum speed of the particle is 4 units (b) Particle further comes to rest at x = 4 (c) Particle oscillates about x = 2 (d) Particle will continuously accelerate along the x-axis.

$$\mathrm{Acceleration}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{which}\:\mathrm{is}\:\mathrm{at} \\ $$$$\mathrm{rest}\:\mathrm{at}\:{x}\:=\:\mathrm{0}\:\mathrm{is}\:\overset{\rightarrow} {{a}}\:=\:\left(\mathrm{4}\:−\:\mathrm{2}{x}\right)\:\overset{\wedge} {{i}}.\:\mathrm{Select} \\ $$$$\mathrm{the}\:\mathrm{correct}\:\mathrm{alternative}\left(\mathrm{s}\right). \\ $$$$\left({a}\right)\:\mathrm{Maximum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is} \\ $$$$\mathrm{4}\:\mathrm{units} \\ $$$$\left({b}\right)\:\mathrm{Particle}\:\mathrm{further}\:\mathrm{comes}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{at} \\ $$$${x}\:=\:\mathrm{4} \\ $$$$\left({c}\right)\:\mathrm{Particle}\:\mathrm{oscillates}\:\mathrm{about}\:{x}\:=\:\mathrm{2} \\ $$$$\left({d}\right)\:\mathrm{Particle}\:\mathrm{will}\:\mathrm{continuously}\:\mathrm{accelerate} \\ $$$$\mathrm{along}\:\mathrm{the}\:{x}-\mathrm{axis}. \\ $$

Question Number 20836 Answers: 0 Comments: 0