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Question Number 196774 Answers: 1 Comments: 0

A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)

$$ \\ $$A man standing on top of Burj Khalifa. If the height of Burj Khalifa including a man is 830 m, then what is the maximum distance up to which a man can see objects on Earth? (Earth's radius 6371 km)

Question Number 196770 Answers: 1 Comments: 2

Question Number 196766 Answers: 0 Comments: 2

Question Number 196621 Answers: 1 Comments: 0

find f(x) if f(x+(√(x^2 +1))) = (x/(x+1))

$$\mathrm{find}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:\mathrm{if} \\ $$$$\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\:=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$

Question Number 196619 Answers: 1 Comments: 0

Question Number 196596 Answers: 0 Comments: 1

If f(x) = ln(((1 + x)/(1 − x))) then prove that f(((2x)/(1 + x^2 ))) = 2f(x).

$$\mathrm{If}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\frac{\mathrm{1}\:+\:{x}}{\mathrm{1}\:−\:{x}}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}\left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:=\:\mathrm{2}{f}\left({x}\right). \\ $$

Question Number 196595 Answers: 0 Comments: 0

Question Number 196594 Answers: 2 Comments: 0

Question Number 196629 Answers: 1 Comments: 1

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 196582 Answers: 1 Comments: 0

If x = log_a bc, y = log_b ca and z = log_c ab then prove that x + y + z = xyz − 2.

$$\mathrm{If}\:{x}\:=\:\mathrm{log}_{{a}} {bc},\:{y}\:=\:\mathrm{log}_{{b}} {ca}\:\mathrm{and}\:{z}\:=\:\mathrm{log}_{{c}} {ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{x}\:+\:{y}\:+\:{z}\:=\:{xyz}\:−\:\mathrm{2}. \\ $$

Question Number 197585 Answers: 4 Comments: 0

f (x)=f((1/x)) ⇒ f(x)=?

$$\mathrm{f}\: \left(\mathrm{x}\right)=\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right) \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 196576 Answers: 1 Comments: 1

Question Number 196571 Answers: 2 Comments: 0

Question Number 196567 Answers: 0 Comments: 3

Show that (((1+ itanθ)/(1− itanθ)))^n =((1+ itan(nθ))/(1− tan(nθ)))

$$\mathrm{Show}\:\mathrm{that}\:\left(\frac{\mathrm{1}+\:\mathrm{itan}\theta}{\mathrm{1}−\:\mathrm{itan}\theta}\right)^{\mathrm{n}} =\frac{\mathrm{1}+\:\mathrm{itan}\left(\mathrm{n}\theta\right)}{\mathrm{1}−\:\mathrm{tan}\left(\mathrm{n}\theta\right)} \\ $$

Question Number 196565 Answers: 1 Comments: 0

find the power series exponition of f(z)=((2z+1)/(z^2 −3z+2)) about z_o = i

$${find}\:{the}\:{power}\:{series}\:{exponition}\:{of}\: \\ $$$${f}\left({z}\right)=\frac{\mathrm{2}{z}+\mathrm{1}}{{z}^{\mathrm{2}} −\mathrm{3}{z}+\mathrm{2}}\:\:{about}\:{z}_{{o}} \:=\:{i} \\ $$

Question Number 196560 Answers: 2 Comments: 1

Question Number 196559 Answers: 0 Comments: 0

Question Number 196558 Answers: 0 Comments: 0

Question Number 196557 Answers: 1 Comments: 0

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(? ,? ,?)

Question Number 196534 Answers: 2 Comments: 0

lim_(x→∞) x (√(1−cos ((π/x)))) =?

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

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