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Question Number 156710    Answers: 1   Comments: 4

Question Number 156671    Answers: 2   Comments: 0

Question Number 156509    Answers: 1   Comments: 5

Question Number 156508    Answers: 1   Comments: 0

Question Number 156335    Answers: 1   Comments: 1

Question Number 156316    Answers: 3   Comments: 1

Question Number 155927    Answers: 0   Comments: 1

Question Number 156184    Answers: 2   Comments: 1

Question Number 155692    Answers: 1   Comments: 5

Question Number 155625    Answers: 2   Comments: 0

lim_(x→0) (((tanx)/x))^(1/x^2 ) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} =\:? \\ $$

Question Number 155574    Answers: 1   Comments: 0

The mean and standard deviation of 20 observation are found to be 10 and 2 respectively .On rechecking it was found that an observation 8 was incorrect.Calculate the incorrect mean and standard deviation (a)If the wrong iterm was ommited (b) If it is replaced by 12

$$\mathrm{The}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation} \\ $$$$\mathrm{of}\:\mathrm{20}\:\mathrm{observation}\:\:\mathrm{are}\:\mathrm{found}\:\mathrm{to}\:\mathrm{be}\: \\ $$$$\mathrm{10}\:\mathrm{and}\:\mathrm{2}\:\mathrm{respectively}\:.\mathrm{On}\:\mathrm{rechecking} \\ $$$$\mathrm{it}\:\mathrm{was}\:\mathrm{found}\:\mathrm{that}\:\:\mathrm{an}\:\mathrm{observation} \\ $$$$\mathrm{8}\:\mathrm{was}\:\mathrm{incorrect}.\mathrm{Calculate}\:\mathrm{the}\:\mathrm{incorrect} \\ $$$$\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\:\mathrm{deviation} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{I}}\mathrm{f}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{wrong}}\:\boldsymbol{\mathrm{iterm}}\:\boldsymbol{\mathrm{was}}\:\:\boldsymbol{\mathrm{ommited}} \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{replaced}}\:\boldsymbol{\mathrm{by}}\:\mathrm{12} \\ $$

Question Number 154353    Answers: 1   Comments: 4

Question Number 154330    Answers: 1   Comments: 0

Question Number 154321    Answers: 2   Comments: 0

Question Number 154172    Answers: 0   Comments: 1

Question Number 153580    Answers: 1   Comments: 0

Question Number 153108    Answers: 1   Comments: 0

∫(dθ/(sin^2 θ(3−sin θ)))

$$\int\frac{\mathrm{d}\theta}{\mathrm{sin}\:^{\mathrm{2}} \theta\left(\mathrm{3}−\mathrm{sin}\:\theta\right)} \\ $$

Question Number 152985    Answers: 0   Comments: 2

Question Number 152829    Answers: 2   Comments: 0

Question Number 151934    Answers: 1   Comments: 0

Question Number 151893    Answers: 1   Comments: 0

∫x(x^3 +a^3 )dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} +\mathrm{a}^{\mathrm{3}} \right)\mathrm{dx} \\ $$

Question Number 151561    Answers: 1   Comments: 0

Given that x+iy=(a/(b+sin θ+icos θ)) show that (b^2 −1)(x^2 +y^2 )+a^2 =2abx

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{x}+\mathrm{iy}=\frac{\mathrm{a}}{\mathrm{b}+\mathrm{sin}\:\theta+\mathrm{icos}\:\theta} \\ $$$$\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{b}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)+\mathrm{a}^{\mathrm{2}} =\mathrm{2abx} \\ $$

Question Number 151496    Answers: 1   Comments: 0

∀x,y∈R_+ ^∗ , show that (x/(x^4 +y^2 ))+(y/(y^4 +x^2 ))≤(1/(xy))

$$\forall{x},{y}\in\mathbb{R}_{+} ^{\ast} ,\:{show}\:{that}\:\frac{{x}}{{x}^{\mathrm{4}} +{y}^{\mathrm{2}} }+\frac{{y}}{{y}^{\mathrm{4}} +{x}^{\mathrm{2}} }\leqslant\frac{\mathrm{1}}{{xy}} \\ $$

Question Number 151444    Answers: 2   Comments: 0

Question Number 151036    Answers: 0   Comments: 0

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Question Number 150405    Answers: 2   Comments: 0

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