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Question Number 165725 Answers: 1 Comments: 0

Show that : ∀ k ∈ N^(∗ ) , (1/(k+1))≤ln(k+1)−ln(k)≤(1/k)

$${Show}\:{that}\::\:\forall\:{k}\:\in\:\mathbb{N}^{\ast\:} ,\: \\ $$$$\frac{\mathrm{1}}{{k}+\mathrm{1}}\leqslant{ln}\left({k}+\mathrm{1}\right)−{ln}\left({k}\right)\leqslant\frac{\mathrm{1}}{{k}} \\ $$

Question Number 165724 Answers: 2 Comments: 0

(U_n )_(n∈N^∗ ) : U_n =Σ_(k=1) ^n (1/k) Show that ∀ n∈N^(∗ ) , U_(2n) −U_n ≥(1/2) . Deduct that lim_(n→+∞) U_n =+∞

$$\left({U}_{{n}} \right)_{{n}\in\mathbb{N}^{\ast} } \::\:{U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\: \\ $$$${Show}\:{that}\:\forall\:{n}\in\mathbb{N}^{\ast\:} ,\:{U}_{\mathrm{2}{n}} −{U}_{{n}} \geqslant\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$.\:{Deduct}\:{that}\:\underset{{n}\rightarrow+\infty} {{lim}}\:{U}_{{n}} =+\infty \\ $$

Question Number 165722 Answers: 1 Comments: 1

Question Number 165699 Answers: 1 Comments: 1

lim_(x→2) ((x−(√(x+2)))/( (√(4x+1)) −3))=....???

$${li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{{x}−\sqrt{{x}+\mathrm{2}}}{\:\sqrt{\mathrm{4}{x}+\mathrm{1}}\:−\mathrm{3}}=....??? \\ $$

Question Number 165698 Answers: 1 Comments: 0

Question Number 165687 Answers: 2 Comments: 0

If f(x)= ((x^( 2) − 2x −8)/(x^( 2) −7x +12)) then ,find : f^( −1) (x)=?

$$ \\ $$$$\:\:\mathrm{I}{f}\:\:\:\:{f}\left({x}\right)=\:\frac{{x}^{\:\mathrm{2}} −\:\mathrm{2}{x}\:−\mathrm{8}}{{x}^{\:\mathrm{2}} −\mathrm{7}{x}\:+\mathrm{12}} \\ $$$$\:\:\:{then}\:,{find}\::\:\:\:\:\:\:\:\:\:\:\:{f}^{\:−\mathrm{1}} \left({x}\right)=? \\ $$$$ \\ $$

Question Number 165685 Answers: 2 Comments: 0

_0 ∫^2 ∣ x^2 −2x+1 ∣ dx =?

$$\:_{\mathrm{0}} \int^{\mathrm{2}} \mid\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}\:\mid\:{dx}\:=?\: \\ $$

Question Number 165713 Answers: 1 Comments: 0

Question Number 165731 Answers: 1 Comments: 2

∫ (√(sinx)) dx

$$\int\:\sqrt{{sinx}}\:{dx} \\ $$

Question Number 165673 Answers: 1 Comments: 0

Question Number 165672 Answers: 0 Comments: 0

Question Number 165670 Answers: 0 Comments: 0

Question Number 165669 Answers: 1 Comments: 1

Question Number 165751 Answers: 1 Comments: 0

x^3 +6x−9=0 ⇒x=?

$$\:\mathrm{x}^{\mathrm{3}} +\mathrm{6x}−\mathrm{9}=\mathrm{0}\:\Rightarrow\mathrm{x}=? \\ $$

Question Number 165653 Answers: 1 Comments: 2

Question Number 165651 Answers: 1 Comments: 5

If the equation (2x−1)−p(x^2 +2)=0, where p is constant, has imaginary roots, deduce that 2p^2 +p−1≥0.

$${If}\:{the}\:{equation}\:\left(\mathrm{2}{x}−\mathrm{1}\right)−{p}\left({x}^{\mathrm{2}} +\mathrm{2}\right)=\mathrm{0}, \\ $$$${where}\:{p}\:{is}\:{constant},\:{has}\:{imaginary} \\ $$$${roots},\:{deduce}\:{that}\:\mathrm{2}{p}^{\mathrm{2}} +{p}−\mathrm{1}\geqslant\mathrm{0}. \\ $$

Question Number 165650 Answers: 0 Comments: 0

Question Number 165649 Answers: 0 Comments: 0

Question Number 165648 Answers: 0 Comments: 0

Question Number 165639 Answers: 1 Comments: 1

Question Number 165692 Answers: 1 Comments: 0

why we use the current as conventional in a circuit?

$${why}\:{we}\:{use}\:{the}\:{current}\:{as}\:{conventional}\:{in} \\ $$$${a}\:{circuit}? \\ $$

Question Number 165691 Answers: 1 Comments: 0

why can′t birds catch by the AC current?

$${why}\:{can}'{t}\:{birds}\:{catch}\:{by}\:{the}\:{AC}\:{current}? \\ $$

Question Number 165637 Answers: 1 Comments: 0

37tanx =11tan3x solve it

$$\mathrm{37}{tanx}\:=\mathrm{11}{tan}\mathrm{3}{x} \\ $$$${solve}\:{it} \\ $$

Question Number 165620 Answers: 1 Comments: 0

solve z^7 =−4

$${solve} \\ $$$${z}^{\mathrm{7}} =−\mathrm{4} \\ $$

Question Number 165617 Answers: 1 Comments: 0

what is the focal length formula for combined lenses? if lenses more than tow?

$${what}\:{is}\:{the}\:{focal}\:{length}\:{formula}\:{for}\: \\ $$$${combined}\:{lenses}?\:{if}\:{lenses}\:{more}\:{than}\: \\ $$$${tow}? \\ $$

Question Number 165616 Answers: 2 Comments: 1

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