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Question Number 118627 Answers: 1 Comments: 0

find the infmum(s) if S=Σ_(n=1) ^∞ (((−1)^n )/(n )) help me sir

$${find}\:{the}\:{infmum}\left({s}\right)\:{if}\:{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\:}\: \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 118612 Answers: 1 Comments: 0

Question Number 118606 Answers: 0 Comments: 0

Question Number 118594 Answers: 0 Comments: 0

Question Number 118588 Answers: 1 Comments: 1

x(x+y) dy −x^2 dx = 0

$${x}\left({x}+{y}\right)\:{dy}\:−{x}^{\mathrm{2}} \:{dx}\:=\:\mathrm{0}\: \\ $$

Question Number 118585 Answers: 0 Comments: 4

v2.227 reverts app first screen to two parts, saved and forum. To start in forum by default change settings and Enable start in forum. Non English users were having difficulty in locating offline editor. Work is in progress to translate in-app menu to different languages.

$${v}\mathrm{2}.\mathrm{227}\:\mathrm{reverts}\:\mathrm{app}\:\mathrm{first}\:\mathrm{screen}\:\mathrm{to} \\ $$$$\mathrm{two}\:\mathrm{parts},\:\mathrm{saved}\:\mathrm{and}\:\mathrm{forum}. \\ $$$$\mathrm{To}\:\mathrm{start}\:\mathrm{in}\:\mathrm{forum}\:\mathrm{by}\:\mathrm{default}\:\mathrm{change} \\ $$$$\mathrm{settings}\:\mathrm{and}\:\mathrm{Enable}\:\mathrm{start}\:\mathrm{in}\:\mathrm{forum}. \\ $$$$\mathrm{Non}\:\mathrm{English}\:\mathrm{users}\:\mathrm{were}\:\mathrm{having} \\ $$$$\mathrm{difficulty}\:\mathrm{in}\:\mathrm{locating}\:\mathrm{offline}\:\mathrm{editor}. \\ $$$$\mathrm{Work}\:\mathrm{is}\:\mathrm{in}\:\mathrm{progress}\:\mathrm{to}\:\mathrm{translate} \\ $$$$\mathrm{in}-\mathrm{app}\:\mathrm{menu}\:\mathrm{to}\:\mathrm{different}\:\mathrm{languages}. \\ $$

Question Number 118575 Answers: 1 Comments: 0

∫ cos (2cot^(−1) (√((1−x)/(1+x))) ) dx ?

$$\:\:\int\:\mathrm{cos}\:\left(\mathrm{2cot}^{−\mathrm{1}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\:\right)\:{dx}\:? \\ $$

Question Number 118574 Answers: 1 Comments: 0

find particular solution of (D^3 +4D) y = sin 2x by using inverse operation ?

$${find}\:{particular}\:{solution}\:{of}\: \\ $$$$\left({D}^{\mathrm{3}} +\mathrm{4}{D}\right)\:{y}\:=\:\mathrm{sin}\:\mathrm{2}{x}\:{by}\:{using} \\ $$$${inverse}\:{operation}\:? \\ $$

Question Number 118570 Answers: 2 Comments: 0

Find the dimensions of the largest rectangular garden that can be enclosed by 80m of fencing

$${Find}\:{the}\:{dimensions}\:{of}\:{the} \\ $$$${largest}\:{rectangular}\:{garden}\:{that} \\ $$$${can}\:{be}\:{enclosed}\:{by}\:\mathrm{80}{m}\:{of} \\ $$$${fencing} \\ $$

Question Number 118566 Answers: 6 Comments: 2

solve ∫_0 ^1 (dx/( (√x) (√(1−x)) )) .

$$\:\:{solve}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{{x}}\:\sqrt{\mathrm{1}−{x}}\:}\:. \\ $$

Question Number 118555 Answers: 2 Comments: 0

Question Number 118545 Answers: 1 Comments: 1

Question Number 118541 Answers: 3 Comments: 1

∫ tan (x).tan (2x).tan (3x) dx = ?

$$\:\:\:\int\:\mathrm{tan}\:\left({x}\right).\mathrm{tan}\:\left(\mathrm{2}{x}\right).\mathrm{tan}\:\left(\mathrm{3}{x}\right)\:{dx}\:=\:? \\ $$

Question Number 118546 Answers: 3 Comments: 7

nilai maksimum?fungsi y= 1+ sin 2x +cos 2x

$${nilai}\:{maksimum}?{fungsi}\:{y}=\:\mathrm{1}+\:{sin}\:\mathrm{2}{x}\:+{cos}\:\mathrm{2}{x} \\ $$

Question Number 118513 Answers: 2 Comments: 0

If f(x) + f(((x − 1)/x)) = 1 + x, find f(2).

$$\mathrm{If}\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:\:+\:\:\mathrm{f}\left(\frac{\mathrm{x}\:\:−\:\:\mathrm{1}}{\mathrm{x}}\right)\:\:\:=\:\:\:\mathrm{1}\:\:+\:\:\mathrm{x},\:\:\:\:\:\:\:\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right). \\ $$

Question Number 121164 Answers: 0 Comments: 0

...ADVANCED CALCULUS... If ∫_0 ^( ∞) ln(x)sin(x^2 )dx =λ∫_0 ^( ∞) sin(x^2 )dx then find the value of ′′λ′′ . ...m.n.july.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{ADVANCED}\:\:\mathrm{CALCULUS}... \\ $$$$\:\:\:\:\mathrm{If}\:\:\:\int_{\mathrm{0}} ^{\:\infty} {ln}\left({x}\right){sin}\left({x}^{\mathrm{2}} \right){dx}\:=\lambda\int_{\mathrm{0}} ^{\:\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}\: \\ $$$$\:\:\:\:\:\:\:\:{then}\:\:{find}\:\:{the}\:\:{value}\:{of}\:''\lambda''\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{m}.\mathrm{n}.\mathrm{july}.\mathrm{1970}... \\ $$

Question Number 118506 Answers: 2 Comments: 0

Question Number 118511 Answers: 3 Comments: 0

How many positive integers x satisfy log_(x/8) (x^2 /4)<7+log_2 (8/x)

$$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:{x}\:\mathrm{satisfy} \\ $$$$\mathrm{log}_{\frac{{x}}{\mathrm{8}}} \frac{{x}^{\mathrm{2}} }{\mathrm{4}}<\mathrm{7}+\mathrm{log}_{\mathrm{2}} \frac{\mathrm{8}}{{x}} \\ $$

Question Number 118491 Answers: 1 Comments: 0

... ⧫Advanced Calculus⧫... Evaluate:: Ω = ∫_0 ^( ∞) ((secθ)/( (√(4tan^2 θ+5))))dθ ...♠L𝛗rD ∅sE♠... ...♣GooD LucK♣

$$ \\ $$$$...\:\blacklozenge\mathrm{Advanced}\:\mathrm{Calculus}\blacklozenge... \\ $$$$ \\ $$$$\mathrm{Evaluate}:: \\ $$$$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sec}\theta}{\:\sqrt{\mathrm{4tan}^{\mathrm{2}} \theta+\mathrm{5}}}\mathrm{d}\theta \\ $$$$ \\ $$$$...\spadesuit\boldsymbol{\mathrm{L}\phi\mathrm{rD}}\:\boldsymbol{\varnothing\mathrm{sE}}\spadesuit... \\ $$$$ \\ $$$$...\clubsuit\boldsymbol{\mathrm{GooD}}\:\boldsymbol{\mathrm{LucK}}\clubsuit \\ $$

Question Number 118489 Answers: 2 Comments: 0

(1) solve the equation ((x−49)/(50)) + ((x−50)/(49)) = ((49)/(x−50)) + ((50)/(x−49)) (2) How many numbers from 12 to 12345 inclusive have digits which are consecutive an in increasing order, reading from left to right ?

$$\left(\mathrm{1}\right)\:{solve}\:{the}\:{equation}\:\frac{{x}−\mathrm{49}}{\mathrm{50}}\:+\:\frac{{x}−\mathrm{50}}{\mathrm{49}}\:=\:\frac{\mathrm{49}}{{x}−\mathrm{50}}\:+\:\frac{\mathrm{50}}{{x}−\mathrm{49}} \\ $$$$\left(\mathrm{2}\right)\:{How}\:{many}\:{numbers}\:{from}\:\mathrm{12}\:{to}\:\mathrm{12345}\: \\ $$$${inclusive}\:{have}\:{digits}\:{which}\:{are}\: \\ $$$${consecutive}\:{an}\:{in}\:{increasing}\:{order}, \\ $$$${reading}\:{from}\:{left}\:{to}\:{right}\:?\: \\ $$

Question Number 118488 Answers: 1 Comments: 0

Conjecture a formula for the infinite sum of the series. (1/3)+(1/(15))+(1/(35))+ ∙ ∙ ∙ (1/((2n−1)(2n+1))) And prove the formula by Induction.

Question Number 118482 Answers: 1 Comments: 0

If the tangents at the end of a focal chord of parabola meet the tangent at the vertex in C,D.prove that CD substends a right angle at the focus

$$\mathrm{If}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{focal}\:\:\mathrm{chord}\:\mathrm{of} \\ $$$$\mathrm{parabola}\:\mathrm{meet}\:\mathrm{the} \\ $$$$\mathrm{tangent}\:\mathrm{at}\:\mathrm{the}\:\:\mathrm{vertex} \\ $$$$\mathrm{in}\:\mathrm{C},\mathrm{D}.\mathrm{prove}\:\mathrm{that}\:\mathrm{CD} \\ $$$$\mathrm{substends}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{focus} \\ $$

Question Number 118478 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−2x) ln(1+3x)dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{3x}\right)\mathrm{dx} \\ $$

Question Number 118476 Answers: 0 Comments: 0

find ∫_(−∞) ^∞ ((arctan(1+2x))/(x^2 +1))dx

$$\mathrm{find}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$