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Question Number 196555    Answers: 0   Comments: 0

In △ABC show that Σ ((1 + cos ∙ (A − B) ∙ cos C)/(h_C ∙ sec C)) = (3/(2 R))

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\Sigma\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\centerdot\:\left(\mathrm{A}\:−\:\mathrm{B}\right)\:\centerdot\:\mathrm{cos}\:\mathrm{C}}{\mathrm{h}_{\boldsymbol{\mathrm{C}}} \:\centerdot\:\mathrm{sec}\:\mathrm{C}}\:\:=\:\:\frac{\mathrm{3}}{\mathrm{2}\:\mathrm{R}} \\ $$

Question Number 196614    Answers: 2   Comments: 0

if S_n =(1/(1+5n))+(1/(2+5n))+(1/(3+5n))+...+(1/(6n)), find lim_(n→∞) S_n =?

$${if}\:{S}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}+\mathrm{5}{n}}+\frac{\mathrm{1}}{\mathrm{2}+\mathrm{5}{n}}+\frac{\mathrm{1}}{\mathrm{3}+\mathrm{5}{n}}+...+\frac{\mathrm{1}}{\mathrm{6}{n}}, \\ $$$${find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{S}_{{n}} =? \\ $$

Question Number 196612    Answers: 0   Comments: 1

Question Number 196544    Answers: 1   Comments: 0

Question Number 196540    Answers: 1   Comments: 0

using definition of limit, prove lim_(x→+∞) (x/(x+1)) = 1

$$\:\:{using}\:{definition}\:{of}\:{limit},\:{prove}\: \\ $$$$\:\:\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}}{{x}+\mathrm{1}}\:=\:\mathrm{1} \\ $$

Question Number 196539    Answers: 0   Comments: 0

Σ_(i=1) ^6 f(i)=Σ_(i=1) ^6 f(6+1−i) Σ_(i=1) ^6 Σ_(j=1) ^i f(i,j)=Σ_(i=1) ^6 Σ_(j=1) ^i f(6+1−j,6+1−i) Σ_(i=1) ^6 Σ_(j=1) ^i Σ_(k=1) ^j f(i,j,k)=Σ_(i=1) ^6 Σ_(j=1) ^i Σ_(k=1) ^j f(? ,? ,?)

$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{f}\left({i}\right)=\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{f}\left(\mathrm{6}+\mathrm{1}−{i}\right) \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{i}} {\sum}}{f}\left({i},{j}\right)=\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{i}} {\sum}}{f}\left(\mathrm{6}+\mathrm{1}−{j},\mathrm{6}+\mathrm{1}−{i}\right) \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{i}} {\sum}}\underset{{k}=\mathrm{1}} {\overset{{j}} {\sum}}{f}\left({i},{j},{k}\right)=\underset{{i}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}\underset{{j}=\mathrm{1}} {\overset{{i}} {\sum}}\underset{{k}=\mathrm{1}} {\overset{{j}} {\sum}}{f}\left(?\:,?\:,?\right) \\ $$

Question Number 196534    Answers: 2   Comments: 0

lim_(x→∞) x (√(1−cos ((π/x)))) =?

$$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\:\sqrt{\mathrm{1}−\mathrm{cos}\:\left(\frac{\pi}{\mathrm{x}}\right)}\:=? \\ $$

Question Number 196525    Answers: 1   Comments: 0

Question Number 196523    Answers: 2   Comments: 0

resoudre dans c l equation sinx=2 ★erly rolvinst★ <erly rolvinst>

$${resoudre}\:{dans}\:{c}\:{l}\:{equation}\:{sinx}=\mathrm{2}\:\:\:\:\:\bigstar{erly}\:{rolvinst}\bigstar\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:<{erly}\:{rolvinst}> \\ $$

Question Number 196522    Answers: 1   Comments: 0

Prove that ∀n∈N ∫^( n+1) _( n) lnt dt ≤ ln(∫^( n+1) _n t dt)

$$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\in\mathbb{N} \\ $$$$\underset{\:\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{ln}{t}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} {t}\:\mathrm{dt}\right) \\ $$

Question Number 196519    Answers: 1   Comments: 0

if xyz=1, prove ((x/(x−1)))^2 +((y/(y−1)))^2 +((z/(z−1)))^2 ≥1.

$${if}\:{xyz}=\mathrm{1},\:{prove} \\ $$$$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{y}}{{y}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{z}}{{z}−\mathrm{1}}\right)^{\mathrm{2}} \geqslant\mathrm{1}. \\ $$

Question Number 196518    Answers: 1   Comments: 0

resouxre cosx=2

$${resouxre}\:{cosx}=\mathrm{2} \\ $$

Question Number 196517    Answers: 1   Comments: 0

Question Number 196516    Answers: 1   Comments: 0

Question Number 196515    Answers: 1   Comments: 0

Find: ∫_0 ^( +∞) x^𝛑 e^(−x) dx = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:+\infty} \:\mathrm{x}^{\boldsymbol{\pi}} \:\mathrm{e}^{−\boldsymbol{\mathrm{x}}} \:\mathrm{dx}\:=\:? \\ $$

Question Number 196504    Answers: 0   Comments: 0

Question Number 196498    Answers: 1   Comments: 0

Question Number 196496    Answers: 1   Comments: 0

Question Number 196493    Answers: 1   Comments: 1

Question Number 196491    Answers: 1   Comments: 2

Question Number 196489    Answers: 0   Comments: 0

Question Number 196487    Answers: 1   Comments: 0

∫(sec^4 x−cot^4 x)dx

$$\int\left(\mathrm{sec}\:^{\mathrm{4}} {x}−\mathrm{cot}\:^{\mathrm{4}} {x}\right){dx} \\ $$

Question Number 196486    Answers: 0   Comments: 0

Question Number 196485    Answers: 1   Comments: 1

Σ_(k=o) ^n (−1)^k =?

$$\underset{{k}={o}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:=? \\ $$

Question Number 196483    Answers: 0   Comments: 0

Question Number 196471    Answers: 1   Comments: 0

lim_(n→∞) (1/n)((1/(2 + (1/n))) + (1/(2 + (2/n))) + (1/(2 + (3/n))) + .. + (1/(2 + (n/n))))

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}}\left(\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{2}}{\mathrm{n}}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{3}}{\mathrm{n}}}\:\:+\:\:..\:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{n}}{\mathrm{n}}}\right) \\ $$

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