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AllQuestion and Answers: Page 1080

Question Number 109817 Answers: 0 Comments: 1

Question Number 109806 Answers: 0 Comments: 0

a handy little formula to remember in case you forget the value of 3 :) ^(2/((((log_2 (3))/2)))) (√2^4 )=3

$$\mathrm{a}\:\mathrm{handy}\:\mathrm{little}\:\mathrm{formula}\:\mathrm{to}\:\mathrm{remember} \\ $$$$\left.\mathrm{in}\:\mathrm{case}\:\mathrm{you}\:\mathrm{forget}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}\::\right) \\ $$$$ \\ $$$$\:\:\:^{\frac{\mathrm{2}}{\left(\frac{\mathrm{log}_{\mathrm{2}} \left(\mathrm{3}\right)}{\mathrm{2}}\right)}} \sqrt{\mathrm{2}^{\mathrm{4}} }=\mathrm{3} \\ $$

Question Number 109801 Answers: 0 Comments: 2

calculste ∫_0 ^1 (√(1+x^6 ))dx

$$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{6}} }\mathrm{dx} \\ $$

Question Number 109794 Answers: 0 Comments: 0

Question Number 109787 Answers: 0 Comments: 0

How to prove that ▽×(▽×E)= ▽▽.E−▽^2 E, where E is the eletric field?

$${How}\:{to}\:{prove}\:{that}\:\bigtriangledown×\left(\bigtriangledown×{E}\right)=\:\bigtriangledown\bigtriangledown.{E}−\bigtriangledown^{\mathrm{2}} {E},\:{where}\:{E}\:{is}\:{the}\:{eletric}\:{field}? \\ $$

Question Number 109776 Answers: 0 Comments: 0

Question Number 109775 Answers: 3 Comments: 0

log_a (3x−4a)+log_a 3x=(2/(log_2 a))+log_a (1−2a), where 0<a<(1/2), find the value of x.

$$\mathrm{log}_{{a}} \left(\mathrm{3}{x}−\mathrm{4}{a}\right)+\mathrm{log}_{{a}} \mathrm{3}{x}=\frac{\mathrm{2}}{\mathrm{log}_{\mathrm{2}} {a}}+\mathrm{log}_{{a}} \left(\mathrm{1}−\mathrm{2}{a}\right),\:\mathrm{where}\:\mathrm{0}<{a}<\frac{\mathrm{1}}{\mathrm{2}}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}. \\ $$

Question Number 109769 Answers: 1 Comments: 0

lim_(x→Π) ((1−cos xcos 2xcos 3x)/(1−cos x))=?

$$\underset{{x}\rightarrow\Pi} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=? \\ $$

Question Number 109766 Answers: 1 Comments: 0

lim_(n→∞) ((2^(n/2) +(n+1)!)/(n(3^n +n!)))=?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{{n}}{\mathrm{2}}} +\left({n}+\mathrm{1}\right)!}{{n}\left(\mathrm{3}^{{n}} +{n}!\right)}=? \\ $$

Question Number 109765 Answers: 1 Comments: 0

(x_n )=(((−1)^n n+10)/( (√(n^2 +1)))),n∈N show if the sequence is limited.

$$\left({x}_{{n}} \right)=\frac{\left(−\mathrm{1}\right)^{{n}} {n}+\mathrm{10}}{\:\sqrt{{n}^{\mathrm{2}} +\mathrm{1}}},{n}\in{N}\:\mathrm{show}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{limited}. \\ $$

Question Number 109763 Answers: 3 Comments: 0

lim_(n→∞) ((3/(1−^n (√8)))−(5/(1−^n (√(32)))))=?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{3}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{8}}}−\frac{\mathrm{5}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{32}}}\right)=? \\ $$

Question Number 109760 Answers: 1 Comments: 1

Question Number 109754 Answers: 1 Comments: 0

1.specify value absolute x if ? b.∣2x+3∣+x−3=0

$$\mathrm{1}.{specify}\:{value}\:{absolute}\:{x}\:{if}\:? \\ $$$$ \\ $$$${b}.\mid\mathrm{2}{x}+\mathrm{3}\mid+{x}−\mathrm{3}=\mathrm{0} \\ $$$$ \\ $$

Question Number 109750 Answers: 2 Comments: 0

Question Number 109749 Answers: 1 Comments: 0

Question Number 109746 Answers: 0 Comments: 3

Find the value of Σ_(n = 0) ^(2020) [(2^n /(1 + 3^((2^n )) ))]

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{n}\:=\:\mathrm{0}} {\overset{\mathrm{2020}} {\sum}}\:\left[\frac{\mathrm{2}^{{n}} }{\mathrm{1}\:+\:\mathrm{3}^{\left(\mathrm{2}^{{n}} \right)} }\right] \\ $$

Question Number 109738 Answers: 4 Comments: 1

(((x/y)−(y/x))/((x^2 +2xy+y^2 )/(x^2 −y^2 )))=(9/4) (x/y)=?

$$\frac{\frac{\mathrm{x}}{\mathrm{y}}−\frac{\mathrm{y}}{\mathrm{x}}}{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }}=\frac{\mathrm{9}}{\mathrm{4}} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}=? \\ $$

Question Number 109736 Answers: 1 Comments: 0

please solve : lim_(n→∞) ((1 +(√2) +(3)^(1/3) +(4)^(1/4) +......((2n))^(1/(2n)) )/(3n−4)) =???

$$\:\:\:\:{please}\:{solve}\:: \\ $$$$\:\: \\ $$$${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}\:+\sqrt{\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\sqrt[{\mathrm{4}}]{\mathrm{4}}\:+......\sqrt[{\mathrm{2}{n}}]{\mathrm{2}{n}}}{\mathrm{3}{n}−\mathrm{4}} \\ $$$$=??? \\ $$

Question Number 109724 Answers: 4 Comments: 0

y = (√(x+(√(x+(√x))))) ⇒ (dy/dx) ?

$$\:\:{y}\:=\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}\:\Rightarrow\:\frac{{dy}}{{dx}}\:?\: \\ $$

Question Number 109721 Answers: 1 Comments: 0

Question Number 109722 Answers: 2 Comments: 1

⊸((♭ε)/(math))⊸ lim_(x→0) ((sin x)/( (√(1−cos x)))) = ?

$$\:\:\:\:\:\multimap\frac{\flat\epsilon}{{math}}\multimap \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}\:=\:?\: \\ $$

Question Number 109715 Answers: 1 Comments: 0

{ ((sin 2x+sin 2y=(5/4))),((cos (x−y)=2sin (x+y))) :}where 0<x,y<(π/2) cos^2 (x+y) = ? △((♭o♭)/(hans))▽

$$\begin{cases}{\mathrm{sin}\:\mathrm{2}{x}+\mathrm{sin}\:\mathrm{2}{y}=\frac{\mathrm{5}}{\mathrm{4}}}\\{\mathrm{cos}\:\left({x}−{y}\right)=\mathrm{2sin}\:\left({x}+{y}\right)}\end{cases}{where}\:\mathrm{0}<{x},{y}<\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \left({x}+{y}\right)\:=\:? \\ $$$$\:\:\:\:\:\:\bigtriangleup\frac{\flat{o}\flat}{{hans}}\bigtriangledown \\ $$

Question Number 109734 Answers: 1 Comments: 0

solve the following integral 1)∫_3 ^7 4(√((x−3)(7−x)))dx 2)∫_0 ^∞ ((xln^2 (1+x))/((1+x)^3 ))dx 3)∫_0 ^(π/4) [ln(1−tanx)]^2 dx=(π/2)ln2−2G 4)∫_0 ^(π/4) ln(1+cotx)dx=(π/8)ln2+G 5)∫_0 ^(π/2) ln(2+cosx)dx

$${solve}\:{the}\:{following}\:{integral} \\ $$$$\left.\mathrm{1}\right)\int_{\mathrm{3}} ^{\mathrm{7}} \mathrm{4}\sqrt{\left({x}−\mathrm{3}\right)\left(\mathrm{7}−{x}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\infty} \frac{{x}\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx} \\ $$$$\left.\mathrm{3}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \left[\mathrm{ln}\left(\mathrm{1}−\mathrm{tan}{x}\right)\right]^{\mathrm{2}} {dx}=\frac{\pi}{\mathrm{2}}\mathrm{ln2}−\mathrm{2}{G} \\ $$$$\left.\mathrm{4}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{1}+\mathrm{cot}{x}\right){dx}=\frac{\pi}{\mathrm{8}}\mathrm{ln2}+{G} \\ $$$$\left.\mathrm{5}\right)\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{2}+\mathrm{cos}{x}\right){dx} \\ $$

Question Number 109733 Answers: 2 Comments: 0

lim_(x→0) ((x−tan x)/(sin x−x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}−{x}}\:? \\ $$

Question Number 109709 Answers: 2 Comments: 0

∫_(0 ) ^(π/4) ln(tanx+1)dx

$$\:\:\:\:\:\int_{\mathrm{0}\:} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{tanx}+\mathrm{1}\right)\mathrm{dx} \\ $$

Question Number 109729 Answers: 3 Comments: 0

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