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Question Number 172504    Answers: 2   Comments: 0

Question Number 172498    Answers: 0   Comments: 0

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Question Number 172490    Answers: 0   Comments: 4

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Question Number 172480    Answers: 0   Comments: 0

In acute △ABC holds: Π_(cyc) (tan A)^a ≤ Π_(cyc) (cot (A/2))^((b + c)/2)

$$\mathrm{In}\:\mathrm{acute}\:\bigtriangleup\mathrm{ABC}\:\mathrm{holds}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\left(\mathrm{tan}\:\mathrm{A}\right)^{\boldsymbol{\mathrm{a}}} \:\:\leqslant\:\:\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\left(\mathrm{cot}\:\frac{\mathrm{A}}{\mathrm{2}}\right)^{\frac{\boldsymbol{\mathrm{b}}\:+\:\boldsymbol{\mathrm{c}}}{\mathrm{2}}} \\ $$

Question Number 172468    Answers: 0   Comments: 1

Question Number 172465    Answers: 0   Comments: 1

Question Number 172455    Answers: 1   Comments: 0

using maclaurin′s series exapand (x/2)(((e^x +1)/(e^x −1))) upto x^4 term

$$\mathrm{using}\:\mathrm{maclaurin}'\mathrm{s}\:\mathrm{series}\:\mathrm{exapand} \\ $$$$\frac{{x}}{\mathrm{2}}\left(\frac{{e}^{{x}} +\mathrm{1}}{{e}^{{x}} −\mathrm{1}}\right)\:\mathrm{upto}\:{x}^{\mathrm{4}} \:\mathrm{term} \\ $$

Question Number 172449    Answers: 0   Comments: 0

Question Number 172448    Answers: 1   Comments: 0

Question Number 172453    Answers: 1   Comments: 6

Question Number 172452    Answers: 1   Comments: 0

If , f(x)= ∣ x − k⌊x⌋∣ be one −to−one function on (0,2) find the value of ′′ k ′′.

$$ \\ $$$$\:\:\:\:\:\mathrm{I}{f}\:\:,\:{f}\left({x}\right)=\:\mid\:{x}\:−\:{k}\lfloor{x}\rfloor\mid\:{be}\: \\ $$$$\:{one}\:−{to}−{one}\:{function}\:{on}\:\left(\mathrm{0},\mathrm{2}\right) \\ $$$$\:\:\: \\ $$$$\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:\:\:\:''\:\:\:\:{k}\:\:\:''. \\ $$$$ \\ $$

Question Number 172443    Answers: 2   Comments: 0

Question Number 172439    Answers: 1   Comments: 2

Question Number 172576    Answers: 0   Comments: 0

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Question Number 172450    Answers: 1   Comments: 0

Question Number 172420    Answers: 2   Comments: 0

Question Number 172412    Answers: 2   Comments: 0

Question Number 172409    Answers: 0   Comments: 0

lim_(x→0) ((((1+2sin x))^(1/(sin x)) −((1+tan x))^(1/(tan x)) )/(2x^3 ))=?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{sin}\:{x}}]{\mathrm{1}+\mathrm{2sin}\:{x}}−\sqrt[{\mathrm{tan}\:{x}}]{\mathrm{1}+\mathrm{tan}\:{x}}}{\mathrm{2}{x}^{\mathrm{3}} }=? \\ $$

Question Number 172408    Answers: 1   Comments: 0

Question Number 172404    Answers: 0   Comments: 2

Question Number 172392    Answers: 2   Comments: 2

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