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AllQuestion and Answers: Page 425

Question Number 176768 Answers: 0 Comments: 0

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Question Number 176424 Answers: 0 Comments: 0

Using perseval′s Identity Evaluate : ∫_0 ^∞ (((1−cosx)/x))^2 dx Mastermind

$$\mathrm{Using}\:\mathrm{perseval}'\mathrm{s}\:\mathrm{Identity} \\ $$$$\mathrm{Evaluate}\::\:\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{x}}\right)^{\mathrm{2}} \mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 176423 Answers: 1 Comments: 0

Question Number 176421 Answers: 2 Comments: 0

Question Number 176399 Answers: 2 Comments: 1

a,b,c ∈R_+ ^∗ prove that a+b+c≥3^3 (√(abc))

$$\:{a},{b},{c}\:\in\mathbb{R}_{+} ^{\ast} \:\:{prove}\:{that}\:{a}+{b}+{c}\geqslant\mathrm{3}\:^{\mathrm{3}} \sqrt{{abc}} \\ $$$$ \\ $$

Question Number 176394 Answers: 0 Comments: 1

lim_(x→0) (((1−cos(√(∣x∣)))^2 )/(1−(√(cosx)))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−{cos}\sqrt{\mid{x}\mid}\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{{cosx}}}\:=\:? \\ $$

Question Number 176388 Answers: 1 Comments: 1

find lim_(x→0) ((x+sinx)/(x−sinx))

$$\:{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{sinx}}{{x}−{sinx}} \\ $$

Question Number 176387 Answers: 4 Comments: 5

x^3 +(1/x^3 ) = 1 ⇒(([x^5 +(1/x^5 )]^3 −1)/(x^5 +(1/x^5 ))) =?

$$\:\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{1}\:\Rightarrow\frac{\left[\mathrm{x}^{\mathrm{5}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }\right]^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{5}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }}\:=? \\ $$

Question Number 176384 Answers: 2 Comments: 0

Find the constant term in the expansion of the expression (2+3x)^3 ((1/x)−4)^4

$${Find}\:{the}\:{constant}\:{term}\:{in}\:{the} \\ $$$${expansion}\:{of}\:{the}\:{expression} \\ $$$$\left(\mathrm{2}+\mathrm{3}{x}\right)^{\mathrm{3}} \left(\frac{\mathrm{1}}{{x}}−\mathrm{4}\right)^{\mathrm{4}} \\ $$

Question Number 176393 Answers: 1 Comments: 0

show that 1+2+3+4+................ ∞ = ((−1)/8)

$${show}\:{that} \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+................\:\infty\:=\:\frac{−\mathrm{1}}{\mathrm{8}} \\ $$

Question Number 176391 Answers: 2 Comments: 1

Question Number 176379 Answers: 1 Comments: 0

lineariser sin^5 (x)

$${lineariser}\:{sin}^{\mathrm{5}} \left({x}\right) \\ $$

Question Number 176378 Answers: 0 Comments: 0

Question Number 176375 Answers: 0 Comments: 2

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

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{3}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:=?\: \\ $$

Question Number 176374 Answers: 1 Comments: 0

Show : (∂X/∂Y)∣_Z (∂Y/∂Z)∣_X (∂X/∂Z)∣_Y =−1

$${Show}\:: \\ $$$$\frac{\partial{X}}{\partial{Y}}\mid_{{Z}} \frac{\partial{Y}}{\partial{Z}}\mid_{{X}} \frac{\partial{X}}{\partial{Z}}\mid_{{Y}} =−\mathrm{1} \\ $$

Question Number 176371 Answers: 0 Comments: 1

Question Number 176367 Answers: 1 Comments: 1

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Question Number 176365 Answers: 1 Comments: 0

In △ABC the following relationship holds: Σ_(cyc) (a^2 /(b^2 + c^2 )) + 4 Π_(cyc) cos A ≤ 2

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{relationship}\:\mathrm{holds}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} }\:+\:\mathrm{4}\:\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\mathrm{cos}\:\mathrm{A}\:\leqslant\:\mathrm{2} \\ $$

Question Number 176366 Answers: 1 Comments: 0

donner la forme trigonometrique de(1−i(√)3)(1+i)(cosθ−isinθ)

$${donner}\:{la}\:{forme}\:{trigonometrique}\:{de}\left(\mathrm{1}−{i}\sqrt{}\mathrm{3}\right)\left(\mathrm{1}+{i}\right)\left({cos}\theta−{isin}\theta\right) \\ $$

Question Number 176354 Answers: 2 Comments: 0

Question Number 176336 Answers: 2 Comments: 0

in AB_ ^Δ C : ((b−c)/(h_a )) =k , and A^ is given. B^ , C^ =?

$$ \\ $$$$\:{in}\:{A}\overset{\Delta} {{B}}_{\:} {C}\::\:\:\frac{{b}−{c}}{{h}_{{a}} \:}\:={k}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:{and}\:\:\hat {{A}}\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\:\hat {{B}}\:,\:\hat {{C}}\:=?\:\: \\ $$

Question Number 176334 Answers: 1 Comments: 0

Ψ = ∫_0 ^( 1) (( ln( 1+ x − x^( 2) ))/x)dx = ?

$$ \\ $$$$\:\:\:\:\:\Psi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{ln}\left(\:\mathrm{1}+\:{x}\:−\:{x}^{\:\mathrm{2}} \right)}{{x}}\mathrm{d}{x}\:=\:? \\ $$$$ \\ $$

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