Question and Answers Forum

AllQuestion and Answers: Page 29

Question Number 222511 Answers: 0 Comments: 0

Is the statement correct? in const.“ x+a−bx^n ={0} ” x= { ((−a±((2b)/(n+1)) , n>0)),((N_b ^( a) ∫_b ^( a) G(n−1), n≤0)) :}

$${Is}\:{the}\:{statement}\:{correct}? \\ $$$${in}\:{const}.``\:{x}+{a}−{bx}^{{n}} =\left\{\mathrm{0}\right\}\:'' \\ $$$${x}=\begin{cases}{−{a}\pm\frac{\mathrm{2}{b}}{{n}+\mathrm{1}}\:,\:{n}>\mathrm{0}}\\{{N}_{{b}} ^{\:{a}} \:\int_{{b}} ^{\:{a}} {G}\left({n}−\mathrm{1}\right),\:{n}\leqslant\mathrm{0}}\end{cases} \\ $$

Question Number 222541 Answers: 0 Comments: 3

very very crazy problem, i am not found what is the result of this integral; ∫(1/( (√z) + (√(z−h)) + (√(z−2h)))) dz

$$ \\ $$$$\:\:\:\mathrm{very}\:\mathrm{very}\:\mathrm{crazy}\:\mathrm{problem},\:\:\mathrm{i}\:\mathrm{am}\:\mathrm{not}\:\mathrm{found} \\ $$$$\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}; \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\:\sqrt{{z}}\:+\:\sqrt{{z}−{h}}\:+\:\sqrt{{z}−\mathrm{2}{h}}}\:{dz} \\ $$$$ \\ $$

Question Number 222501 Answers: 1 Comments: 0

This is VERY HARD { ( { ((x+y=0)),((l(y)=1)) :}),( { ((x∈N)),((−y= { ((v%, for x↺γ(1))),((−v%, for x↬θ(∮_(−x) ^( 0) (c/7)))) :})) :}) :} x=?, y=?

$${This}\:{is}\:{VERY}\:{HARD} \\ $$$$\begin{cases}{\begin{cases}{{x}+{y}=\mathrm{0}}\\{{l}\left({y}\right)=\mathrm{1}}\end{cases}}\\{\begin{cases}{{x}\in\mathbb{N}}\\{−{y}=\begin{cases}{{v\%},\:\:{for}\:{x}\circlearrowleft\gamma\left(\mathrm{1}\right)}\\{−{v\%},\:\:{for}\:{x}\looparrowright\theta\left(\oint_{−{x}} ^{\:\mathrm{0}} \frac{{c}}{\mathrm{7}}\right)}\end{cases}}\end{cases}}\end{cases} \\ $$$${x}=?,\:{y}=? \\ $$

Question Number 222512 Answers: 1 Comments: 0

∫_0 ^(π/2) ((xsinxcosx)/(tan^2 x+cotan^2 x))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 222487 Answers: 0 Comments: 0

′Delete all lines′ function deletes all lines without asking after deleting all lines for the first time in the equation editor

$$'{Delete}\:{all}\:{lines}'\:{function}\:{deletes}\:{all}\:{lines}\:{without}\:{asking}\:{after}\:{deleting}\:{all}\:{lines}\:{for}\:{the}\:{first}\:{time}\:{in}\:{the}\:{equation}\:{editor} \\ $$

Question Number 222583 Answers: 0 Comments: 0

solve for p,q,s in terms of c. • (((qs)/(q−sp)))^2 −s(((qs)/(q−sp)))+p=0 • (((q+c)/(p+1)))^2 =sp−q • (q−cp)(p+1)^2 =(q+c)^3 I have to find non zero real x=−(((q+c)/(p+1))) .

$${solve}\:{for}\:{p},{q},{s}\:{in}\:{terms}\:{of}\:{c}. \\ $$$$\bullet\:\left(\frac{{qs}}{{q}−{sp}}\right)^{\mathrm{2}} −{s}\left(\frac{{qs}}{{q}−{sp}}\right)+{p}=\mathrm{0} \\ $$$$\bullet\:\left(\frac{{q}+{c}}{{p}+\mathrm{1}}\right)^{\mathrm{2}} ={sp}−{q} \\ $$$$\bullet\:\left({q}−{cp}\right)\left({p}+\mathrm{1}\right)^{\mathrm{2}} =\left({q}+{c}\right)^{\mathrm{3}} \\ $$$${I}\:{have}\:{to}\:{find}\:{non}\:{zero}\:{real}\:{x}=−\left(\frac{{q}+{c}}{{p}+\mathrm{1}}\right)\:. \\ $$

Question Number 222482 Answers: 2 Comments: 1

Question Number 222479 Answers: 4 Comments: 1

Question Number 222478 Answers: 1 Comments: 0

S=Σ_(n=1) ^∞ (−1)^(n−1) (H_n /n^2 ) = ? note: H_n =1+(1/2) +(1/3) +...+(1/n)

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \frac{{H}_{{n}} }{{n}^{\mathrm{2}} }\:=\:? \\ $$$$\:{note}:\:\:\:{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+...+\frac{\mathrm{1}}{{n}}\: \\ $$

Question Number 222466 Answers: 0 Comments: 4

find the nth term.

$$\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}.\: \\ $$

Question Number 222462 Answers: 2 Comments: 0

i^i =??

$${i}^{{i}} =?? \\ $$

Question Number 222453 Answers: 1 Comments: 0

∫_0 ^( ∞) ((tanh^2 (x))/x^2 ) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{tanh}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$

Question Number 222448 Answers: 0 Comments: 0

∫_0 ^1 ((ln(1+x^2 +(√(x^4 +4x^2 +4))))/(1+x^2 )) dx

$$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} +\sqrt{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$

Question Number 222441 Answers: 2 Comments: 0

0^i

$$\mathrm{0}^{{i}} \\ $$

Question Number 222427 Answers: 1 Comments: 0

if lim_(x→0) (((sin2x)/x^3 )+(a/x^2 )+b)=1 find a and b without using LHopial rule

$$\:\:\boldsymbol{{if}}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\boldsymbol{{sin}}\mathrm{2}\boldsymbol{{x}}}{\boldsymbol{{x}}^{\mathrm{3}} }+\frac{\boldsymbol{{a}}}{\boldsymbol{{x}}^{\mathrm{2}} }+\boldsymbol{{b}}\right)=\mathrm{1}\: \\ $$$$\:\:\:\:\boldsymbol{{find}}\:\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\:\:\boldsymbol{{without}} \\ $$$$\:\:\:\:\:\:\boldsymbol{{using}}\:\boldsymbol{{LH}}{opial}\:{rule} \\ $$

Question Number 222425 Answers: 3 Comments: 0

lim_(x→∞) (4x+(√(16x^2 −3x))) ans:(3/8)

$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\infty} \left(\mathrm{4}\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{16}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}}}\right) \\ $$$$\boldsymbol{\mathrm{ans}}:\frac{\mathrm{3}}{\mathrm{8}} \\ $$

Question Number 222424 Answers: 1 Comments: 0

∫_2 ^( ∞) (dz/(ln(z)))−Σ_(l=2) ^∞ (1/(ln(l)))=??

$$\int_{\mathrm{2}} ^{\:\infty} \:\:\:\:\frac{\mathrm{d}{z}}{\mathrm{ln}\left({z}\right)}−\underset{{l}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{ln}\left({l}\right)}=?? \\ $$

Question Number 222422 Answers: 0 Comments: 0

Prove:∫_0 ^(+∞) ((x^2 lnsinhx)/(cosh 3x))dx=(1/9)π^2 G−(5/(108))π^3 ln 2

$$\mathrm{Prove}:\int_{\mathrm{0}} ^{+\infty} \frac{{x}^{\mathrm{2}} \mathrm{lnsinh}{x}}{\mathrm{cosh}\:\mathrm{3}{x}}{dx}=\frac{\mathrm{1}}{\mathrm{9}}\pi^{\mathrm{2}} {G}−\frac{\mathrm{5}}{\mathrm{108}}\pi^{\mathrm{3}} \mathrm{ln}\:\mathrm{2} \\ $$

Question Number 222419 Answers: 0 Comments: 1

Question Number 222418 Answers: 1 Comments: 0

Prove that: lim_(n→+∞) [ ln^2 (n)−2∫^( n) _( 0) ((lnt)/( (√(1+t^2 )))) dt ]= (π^2 /6)+ln^2 (2)

$$\mathrm{Prove}\:\mathrm{that}:\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left[\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{n}\right)−\mathrm{2}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\:\mathrm{dt}\:\right]=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}+\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$

Question Number 222415 Answers: 3 Comments: 0

Question Number 222432 Answers: 0 Comments: 0

∫_0 ^(π/2) ((xsinxcosx)/(tan^2 x+cotan^2 x))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{xsinxcosx}}{{tan}^{\mathrm{2}} {x}+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 222411 Answers: 3 Comments: 0

[ 1 .] ∫_0 ^( 1) ((ln(x) ln(1−x^2 )ln(1+x^2 ))/(1−x^2 )) dx [ 2 .] ∫_0 ^1 ((ln(x) ln(1−x) ln(1+x) ln(1+x^2 ))/(1+x)) dx [ 3 .] ∫_0 ^1 ((ln(x) ln(1−x^2 ) ln(1+x^2 ))/x) dx [ 4 .] ∫_0 ^( 1) ((ln(x) ln(1−x) ln(1+x) ln(1−x^2 ))/x) dx

Question Number 222568 Answers: 0 Comments: 0

f(x)=((√(x−2)))^0 and g(x)=(√((x−2)^0 )) dom f(x)=? , dom g(x)=?

$${f}\left({x}\right)=\left(\sqrt{{x}−\mathrm{2}}\right)^{\mathrm{0}} \:\:{and}\:{g}\left({x}\right)=\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{0}} } \\ $$$${dom}\:{f}\left({x}\right)=?\:,\:{dom}\:{g}\left({x}\right)=? \\ $$

Question Number 222436 Answers: 1 Comments: 0

Question Number 222409 Answers: 0 Comments: 0

Solve ; ∫_0 ^(π/2) ((ln^n sin θ)/(sin^p θ cos^q θ)) dθ , for n,p,q ∈ R_(≥ 0)

$$ \\ $$$$\:\:\:\mathrm{Solve}\:;\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}^{{n}} \:\mathrm{sin}\:\theta}{\mathrm{sin}^{{p}} \:\theta\:\mathrm{cos}^{{q}} \:\theta}\:\mathrm{d}\theta\:,\:\mathrm{for}\:{n},{p},{q}\:\in\:\mathbb{R}_{\geqslant\:\mathrm{0}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Pg 24 Pg 25 Pg 26 Pg 27 Pg 28 Pg 29 Pg 30 Pg 31 Pg 32 Pg 33

Contact: info@tinkutara.com