Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 501

Question Number 161755 Answers: 2 Comments: 0

prove that Σ_(n=0) ^∞ (((−1)^n )/(n+1)) = ln2

$${prove}\:{that}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+\mathrm{1}}\:=\:{ln}\mathrm{2} \\ $$

Question Number 161750 Answers: 0 Comments: 2

differenciate xsin xcos x

$${differenciate}\:{x}\mathrm{sin}\:{x}\mathrm{cos}\:{x} \\ $$

Question Number 161748 Answers: 0 Comments: 4

⌋

$$\rfloor \\ $$

Question Number 161747 Answers: 2 Comments: 0

lim_(x→0) ((cos^3 (2x)−cos (x))/(cos^2 (4x)−cos (2x))) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)−\mathrm{cos}\:\left({x}\right)}{\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{4}{x}\right)−\mathrm{cos}\:\left(\mathrm{2}{x}\right)}\:=? \\ $$

Question Number 161745 Answers: 1 Comments: 1

Prove that: 3 (√e) = (1/3) Σ_(k=1) ^∞ [ Σ_(n=0) ^∞ (1/(n!)) ]k2^(-k)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{3}\:\sqrt{\mathrm{e}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left[\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}!}\:\right]\mathrm{k2}^{-\boldsymbol{\mathrm{k}}} \\ $$

Question Number 161744 Answers: 1 Comments: 1

Solve for real numbers: (x/y) + (5/x) + ((y - 5)/5) = ((y + x)/(y + 5)) + ((5 + y)/(5 + x))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}\:+\:\frac{\mathrm{5}}{\mathrm{x}}\:+\:\frac{\mathrm{y}\:-\:\mathrm{5}}{\mathrm{5}}\:=\:\frac{\mathrm{y}\:+\:\mathrm{x}}{\mathrm{y}\:+\:\mathrm{5}}\:+\:\frac{\mathrm{5}\:+\:\mathrm{y}}{\mathrm{5}\:+\:\mathrm{x}} \\ $$

Question Number 161742 Answers: 2 Comments: 1

Question Number 161733 Answers: 1 Comments: 0

Question Number 161723 Answers: 4 Comments: 0

Calculate lim_(x→0) (((1+x.2^x )/(1+x.3^x )))^(1/x^2 ) lim_(x→0) [2e^(x/(x+1)) −1]^((x^2 +1)/x) lim_(x→a) ((x^x −a^a )/(x−a))

$${Calculate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}+{x}.\mathrm{2}^{{x}} }{\mathrm{1}+{x}.\mathrm{3}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\mathrm{2}{e}^{\frac{{x}}{{x}+\mathrm{1}}} −\mathrm{1}\right]^{\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}}} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{{x}} −{a}^{{a}} }{{x}−{a}} \\ $$

Question Number 161706 Answers: 1 Comments: 0

J =∫_0 ^( 1) (( 1−x)/(( 1+x +x^( 2) + x^( 3) )ln(x))) dx=?

$$\: \\ $$$$\mathrm{J}\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{1}−{x}}{\left(\:\mathrm{1}+{x}\:+{x}^{\:\mathrm{2}} +\:{x}^{\:\mathrm{3}} \:\right){ln}\left({x}\right)}\:{dx}=? \\ $$$$ \\ $$

Question Number 161704 Answers: 2 Comments: 1

let n∈N fixed , solve for real numbers [x]{x}=nx

$$\mathrm{let}\:\:\mathrm{n}\in\mathbb{N}\:\:\mathrm{fixed}\:,\:\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\left[\mathrm{x}\right]\left\{\mathrm{x}\right\}=\mathrm{nx} \\ $$

Question Number 161698 Answers: 2 Comments: 6

sin (x+y)=sin x+sin y

$$\:\:\mathrm{sin}\:\left({x}+{y}\right)=\mathrm{sin}\:{x}+\mathrm{sin}\:{y} \\ $$

Question Number 161697 Answers: 1 Comments: 0

Question Number 161687 Answers: 1 Comments: 0

nature of the integral ∫_0 ^1 (1/(t^2 (√(1−t))))dt

$${nature}\:{of}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}−{t}}}{dt} \\ $$

Question Number 161675 Answers: 1 Comments: 0

{ ((2x−y−e^(−x) =0)),((−x+2y−e^(−y) =0)) :} { ((x=?)),((y=?)) :}

$$\:\:\begin{cases}{\mathrm{2}{x}−{y}−{e}^{−{x}} =\mathrm{0}}\\{−{x}+\mathrm{2}{y}−{e}^{−{y}} =\mathrm{0}}\end{cases} \\ $$$$\:\begin{cases}{{x}=?}\\{{y}=?}\end{cases} \\ $$

Question Number 161671 Answers: 2 Comments: 1

Question Number 161666 Answers: 1 Comments: 4

if ((g(5)f(5))/(g(5)+f(5)))=1 then((f(4)+g(4))/(f(4)+1))=? when is Gis a I function and F is a constant

$${if}\:\:\frac{{g}\left(\mathrm{5}\right){f}\left(\mathrm{5}\right)}{{g}\left(\mathrm{5}\right)+{f}\left(\mathrm{5}\right)}=\mathrm{1}\:\:\:{then}\frac{{f}\left(\mathrm{4}\right)+{g}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)+\mathrm{1}}=? \\ $$$${when}\:{is}\:\:\:\:\:{Gis}\:{a}\:{I}\:{function}\:\:{and}\:{F}\:{is}\:{a}\:{constant} \\ $$

Question Number 161665 Answers: 0 Comments: 0

nature de ∫_o ^1 (1/(t^2 (√(1−t))))dt

$${nature}\:{de} \\ $$$$\int_{{o}} ^{\mathrm{1}} \frac{\mathrm{1}}{{t}^{\mathrm{2}} \sqrt{\mathrm{1}−{t}}}{dt} \\ $$

Question Number 161664 Answers: 1 Comments: 0

5sec α −4 tan α = 3cosec α ((3cot α)/(5 tan α−4 sec α)) =?

$$\:\:\mathrm{5sec}\:\alpha\:−\mathrm{4}\:\mathrm{tan}\:\alpha\:=\:\mathrm{3cosec}\:\alpha \\ $$$$\:\:\frac{\mathrm{3cot}\:\alpha}{\mathrm{5}\:\mathrm{tan}\:\alpha−\mathrm{4}\:\mathrm{sec}\:\alpha}\:=?\: \\ $$

Question Number 161660 Answers: 3 Comments: 0

∫_0 ^(π/4) ln(1+(√2)cos(x))dx=???

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \boldsymbol{{ln}}\left(\mathrm{1}+\sqrt{\mathrm{2}}\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\right)\boldsymbol{{dx}}=??? \\ $$

Question Number 161656 Answers: 1 Comments: 3

∫_0 ^1 ((xln(1+x))/(1+x^2 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{{xln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}} \\ $$

Question Number 161652 Answers: 0 Comments: 0

∫_0 ^( 1) ((xlog(a+x))/(1+x^2 ))dx ∀ ∣a∣ ∈ N

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{xlog}\left(\mathrm{a}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\forall\:\mid\mathrm{a}\mid\:\in\:\mathbb{N} \\ $$

Question Number 161703 Answers: 2 Comments: 1

(1)∫ ((sin x−cos x)/( (√(sin 2x)))) dx (2) ∫_0 ^( π/2) cos 7x cos 17x cos 37x dx

$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2}{x}}}\:{dx} \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \mathrm{cos}\:\mathrm{7}{x}\:\mathrm{cos}\:\mathrm{17}{x}\:\mathrm{cos}\:\mathrm{37}{x}\:{dx} \\ $$

Question Number 161646 Answers: 0 Comments: 0

Question Number 161644 Answers: 0 Comments: 2

there is no single greater than symbol the closest to such a symbol is ≪ or ≫ when is tinku tara going to add the single arrow its a very common symbol and should be on this keyboard

$$\: \\ $$$$\:\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{single}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{symbol}\:\: \\ $$$$\:\mathrm{the}\:\mathrm{closest}\:\mathrm{to}\:\mathrm{such}\:\mathrm{a}\:\mathrm{symbol}\:\mathrm{is}\:\ll\:\mathrm{or}\:\gg\:\: \\ $$$$\:\mathrm{when}\:\mathrm{is}\:\mathrm{tinku}\:\mathrm{tara}\:\mathrm{going}\:\mathrm{to}\:\mathrm{add}\:\mathrm{the}\:\mathrm{single}\:\mathrm{arrow}\:\: \\ $$$$\:\mathrm{its}\:\mathrm{a}\:\mathrm{very}\:\mathrm{common}\:\mathrm{symbol}\:\mathrm{and}\:\mathrm{should}\:\mathrm{be}\:\mathrm{on}\:\mathrm{this}\:\mathrm{keyboard}\:\: \\ $$$$\: \\ $$$$\: \\ $$

Question Number 161629 Answers: 0 Comments: 0

Pg 496 Pg 497 Pg 498 Pg 499 Pg 500 Pg 501 Pg 502 Pg 503 Pg 504 Pg 505

Terms of Service

Contact: info@tinkutara.com