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Question Number 62777    Answers: 0   Comments: 1

5^(3x−1) .4^(2x−2) =625

$$\mathrm{5}^{\mathrm{3}{x}−\mathrm{1}} .\mathrm{4}^{\mathrm{2}{x}−\mathrm{2}} =\mathrm{625} \\ $$

Question Number 62763    Answers: 0   Comments: 0

Question Number 62762    Answers: 0   Comments: 0

Question Number 62761    Answers: 0   Comments: 3

if cosθ=((cosA.cosB)/(1−cosA.cosB)) prove that Tan(θ/2)=Tan(A/2).Cot(B/2)

$$\mathrm{if}\:\mathrm{cos}\theta=\frac{\mathrm{cosA}.\mathrm{cosB}}{\mathrm{1}−\mathrm{cosA}.\mathrm{cosB}}\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{Tan}\frac{\theta}{\mathrm{2}}=\mathrm{Tan}\frac{\mathrm{A}}{\mathrm{2}}.\mathrm{Cot}\frac{\mathrm{B}}{\mathrm{2}} \\ $$

Question Number 62759    Answers: 1   Comments: 0

y = x^y (dy/dx) = ?

$${y}\:\:=\:\:{x}^{{y}} \\ $$$$\frac{{dy}}{{dx}}\:\:=\:\:? \\ $$

Question Number 62754    Answers: 1   Comments: 2

1)∫(dx/(1−sin(x))) R solve in(2) (4−x)^4 +x^4 =82

$$\left.\mathrm{1}\right)\int\frac{{dx}}{\mathrm{1}−{sin}\left({x}\right)} \\ $$$$ \\ $$$${R}\:{solve}\:{in}\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\left(\mathrm{4}−{x}\right)^{\mathrm{4}} +{x}^{\mathrm{4}} =\mathrm{82} \\ $$

Question Number 62753    Answers: 1   Comments: 0

The normal at the point P(4cos θ,3sin θ) on the ellipse (x^2 /(16)) +(y^2 /9)=1 meets the x−axis and y−axis at A and B respectively show that locus of the mid−point of AB is an ellipse with the same eccentricity as given ellipse.

$${The}\:{normal}\:{at}\:{the}\:{point} \\ $$$${P}\left(\mathrm{4cos}\:\theta,\mathrm{3sin}\:\theta\right)\:{on}\:{the} \\ $$$${ellipse}\:\frac{{x}^{\mathrm{2}} }{\mathrm{16}}\:+\frac{{y}^{\mathrm{2}} }{\mathrm{9}}=\mathrm{1}\:{meets} \\ $$$${the}\:{x}−{axis}\:{and}\:{y}−{axis} \\ $$$${at}\:{A}\:{and}\:{B}\:{respectively} \\ $$$${show}\:{that}\:{locus}\:{of}\:{the} \\ $$$${mid}−{point}\:{of}\:{AB}\:{is}\:{an} \\ $$$${ellipse}\:{with}\:{the}\:{same} \\ $$$${eccentricity}\:{as}\:{given} \\ $$$${ellipse}. \\ $$

Question Number 62747    Answers: 1   Comments: 0

Are f, g: R→R defined by f(x)= { ((0, x ∈ R\Q)),((x, x ∈Q)) :} g(x)= { ((1, x=0)),((0, x≠0)) :} show that lim_(x→0) f(x)=0 and lim_(y→0) g(y)=0 however lim_(x→0) g(f(x)) does not exist.

$${Are}\:\boldsymbol{{f}},\:\boldsymbol{{g}}:\:\mathbb{R}\rightarrow\mathbb{R}\:{defined}\:{by} \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{0},\:\:\:{x}\:\in\:\mathbb{R}\backslash\mathbb{Q}}\\{{x},\:\:\:{x}\:\in\mathbb{Q}}\end{cases} \\ $$$${g}\left({x}\right)=\begin{cases}{\mathrm{1},\:\:\:{x}=\mathrm{0}}\\{\mathrm{0},\:\:\:\:{x}\neq\mathrm{0}}\end{cases} \\ $$$${show}\:{that}\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{0}\:{and}\:\underset{\boldsymbol{\mathrm{y}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{0} \\ $$$${however}\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\right)\:{does}\:{not}\:{exist}. \\ $$

Question Number 62735    Answers: 1   Comments: 1

Question Number 62732    Answers: 1   Comments: 0

calculate ∫_0 ^(2π) ((cos(2x))/(2cosx −sin(x)))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}{cosx}\:−{sin}\left({x}\right)}{dx}\: \\ $$

Question Number 62731    Answers: 0   Comments: 1

find ∫ (√((x−1)/(x^2 +3)))dx

$${find}\:\int\:\sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{3}}}{dx}\: \\ $$

Question Number 62773    Answers: 2   Comments: 1

Question Number 62712    Answers: 0   Comments: 0

$$ \\ $$

Question Number 62708    Answers: 0   Comments: 2

Question Number 62698    Answers: 1   Comments: 0

Lines 5x+12y−10=0 and 5x−12y−40=0 touch circle C_1 of diameter 6. If the center of C_1 lies in the Ist quadrant, find the equation of circle C_2 which is concentric with C_(1 ) and cuts intercept of length 8 on these lines.

$${Lines}\:\mathrm{5}{x}+\mathrm{12}{y}−\mathrm{10}=\mathrm{0}\:{and}\:\mathrm{5}{x}−\mathrm{12}{y}−\mathrm{40}=\mathrm{0} \\ $$$${touch}\:{circle}\:{C}_{\mathrm{1}} \:{of}\:{diameter}\:\mathrm{6}.\:{If}\:{the}\: \\ $$$${center}\:{of}\:{C}_{\mathrm{1}} \:{lies}\:{in}\:{the}\:{Ist}\:{quadrant}, \\ $$$${find}\:{the}\:{equation}\:{of}\:{circle}\:{C}_{\mathrm{2}} \:{which}\:{is}\: \\ $$$${concentric}\:{with}\:{C}_{\mathrm{1}\:} \:{and}\:{cuts}\:{intercept} \\ $$$${of}\:{length}\:\mathrm{8}\:{on}\:{these}\:{lines}. \\ $$

Question Number 62750    Answers: 0   Comments: 1

An element X has RAM of 88g.when a current of 0.5A was passed through fused chloride of X for 32minutes and 10sec. 0.44g of X was deposited at the cathode (a)number of faraday? (b)write formular of X ions (c)write the formular of OH

$${An}\:{element}\:{X}\:{has}\:{RAM} \\ $$$${of}\:\mathrm{88}{g}.{when}\:{a}\:{current} \\ $$$${of}\:\mathrm{0}.\mathrm{5}{A}\:{was}\:{passed}\:{through} \\ $$$${fused}\:{chloride}\:{of}\:{X}\:{for} \\ $$$$\mathrm{32}{minutes}\:{and}\:\mathrm{10}{sec}. \\ $$$$\mathrm{0}.\mathrm{44}{g}\:{of}\:{X}\:{was}\:{deposited} \\ $$$${at}\:{the}\:{cathode} \\ $$$$\left({a}\right){number}\:{of}\:{faraday}? \\ $$$$\left({b}\right){write}\:{formular}\:{of}\: \\ $$$${X}\:{ions} \\ $$$$\left({c}\right){write}\:{the}\:{formular}\:{of}\:{OH} \\ $$

Question Number 62676    Answers: 1   Comments: 1

Question Number 62672    Answers: 1   Comments: 9

Question Number 62669    Answers: 2   Comments: 0

calculate the value of Σ_(n=0) ^(1947) (1/(2^n +(√2^(1947) )))

$${calculate}\:{the}\:{value}\:{of}\:\underset{{n}=\mathrm{0}} {\overset{\mathrm{1947}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{n}} +\sqrt{\mathrm{2}^{\mathrm{1947}} }} \\ $$

Question Number 62666    Answers: 0   Comments: 0

Question Number 62664    Answers: 1   Comments: 0

Find the nth term 100,92,76,44,......

$${Find}\:{the}\:{nth}\:{term} \\ $$$$\mathrm{100},\mathrm{92},\mathrm{76},\mathrm{44},...... \\ $$

Question Number 62659    Answers: 1   Comments: 3

calculate lim_(n→+∞) (((n!)^n )/n^(n!) )

$${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\frac{\left({n}!\right)^{{n}} }{{n}^{{n}!} } \\ $$

Question Number 62657    Answers: 1   Comments: 2

calculate lim_(x→0) ((ln(1+tan(2x))−ln(cos(3x)))/x^3 )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{{ln}\left(\mathrm{1}+{tan}\left(\mathrm{2}{x}\right)\right)−{ln}\left({cos}\left(\mathrm{3}{x}\right)\right)}{{x}^{\mathrm{3}} } \\ $$

Question Number 62656    Answers: 1   Comments: 1

calculate lim_(n→+∞) (((n+1)^n )/n^(n+1) )

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\frac{\left({n}+\mathrm{1}\right)^{{n}} }{{n}^{{n}+\mathrm{1}} } \\ $$

Question Number 62653    Answers: 1   Comments: 4

∫x(arctan(x))^2 dx ∫((x e^(arctan(x)) )/((1+x^2 )^(3/2) )) dx ∫((arcsin(x))/(√(1+x))) dx

$$\int\mathrm{x}\left(\mathrm{arctan}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{x}\:\mathrm{e}^{\mathrm{arctan}\left(\mathrm{x}\right)} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:\mathrm{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{arcsin}\left(\mathrm{x}\right)}{\sqrt{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx} \\ $$

Question Number 62648    Answers: 0   Comments: 1

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