Question and Answers Forum

AllQuestion and Answers: Page 501

Question Number 159966 Answers: 0 Comments: 2

a y=(√(x+(√(x+(√(x+.....)))))) b y=(√(x(√(x(√(x(√(x.....)))))))) find (dy/dx)

$${a}\:\:\:\:{y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+.....}}} \\ $$$${b}\:\:\:\:\:{y}=\sqrt{{x}\sqrt{{x}\sqrt{{x}\sqrt{{x}.....}}}} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$

Question Number 159962 Answers: 0 Comments: 0

show me: these are the cauchy criterion. please 1.(((n+1)/n)) 2. (1+(1/(2!))+(1/(3!))+...+(1/(n!))) 3. ((−1)^n ) 4. n+(((−1)^n )/n) 5.(1nm)

$${show}\:{me}:\:{these}\:{are}\:{the}\:{cauchy}\:{criterion}.\:{please} \\ $$$$\mathrm{1}.\left(\frac{{n}+\mathrm{1}}{{n}}\right) \\ $$$$\mathrm{2}.\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+...+\frac{\mathrm{1}}{{n}!}\right) \\ $$$$\mathrm{3}.\:\left(\left(−\mathrm{1}\right)^{{n}} \right) \\ $$$$\mathrm{4}.\:{n}+\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}} \\ $$$$\mathrm{5}.\left(\mathrm{1}{nm}\right) \\ $$$$ \\ $$

Question Number 159961 Answers: 4 Comments: 0

if x + (1/x) = 2(√5) then find the value of ((x(x^6 − 1))/(x^8 − 1))

$$\mathrm{if}\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}\sqrt{\mathrm{5}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{x}\left({x}^{\mathrm{6}} \:−\:\mathrm{1}\right)}{{x}^{\mathrm{8}} \:−\:\mathrm{1}} \\ $$

Question Number 159960 Answers: 1 Comments: 0

∫_0 ^( 1) ((3x^3 −x^2 +2x−4)/( (√(x^2 −3x+2)))) dx =?

$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx}\:=?\: \\ $$

Question Number 159958 Answers: 1 Comments: 3

find the area and perimeter of ((x/a))^(2/3) +((y/b))^(2/3) =1

$${find}\:{the}\:{area}\:{and}\:{perimeter}\:{of} \\ $$$$\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{a}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\frac{\boldsymbol{{y}}}{\boldsymbol{{b}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{1} \\ $$

Question Number 159944 Answers: 0 Comments: 4

Question Number 159943 Answers: 1 Comments: 0

Question Number 159942 Answers: 0 Comments: 0

Question Number 159941 Answers: 1 Comments: 1

Question Number 159938 Answers: 1 Comments: 0

Evaluate ∫_1 ^( 4) (√((x−1)/x^5 )) dx.

$$\mathrm{Evaluate}\:\int_{\mathrm{1}} ^{\:\mathrm{4}} \sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{5}} }}\:{dx}. \\ $$

Question Number 159936 Answers: 0 Comments: 0

Prove:: lim_(n→+∞) ^(−) nΣ_(k=n+1) ^n (((−1)^(k−1) )/k)=(1/2)

$$\mathrm{Prove}::\:\:\:\underset{\mathrm{n}\rightarrow+\infty} {\overline {\mathrm{lim}}n}\underset{\mathrm{k}=\mathrm{n}+\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}−\mathrm{1}} }{\mathrm{k}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 159935 Answers: 0 Comments: 0

Prove:: lim_(x→+∞) ^(−) xe^(−x) ∫_1 ^x ((e^t sin t)/t)dt=(1/( (√2)))

$$\mathrm{Prove}::\:\:\:\:\underset{\mathrm{x}\rightarrow+\infty} {\overline {\mathrm{lim}}xe}^{−\mathrm{x}} \int_{\mathrm{1}} ^{\mathrm{x}} \frac{\mathrm{e}^{\mathrm{t}} \mathrm{sin}\:\mathrm{t}}{\mathrm{t}}\mathrm{dt}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$

Question Number 159931 Answers: 0 Comments: 0

Prove :: ∫_0 ^∞ ((sin^n x)/x^m )dx=(1/(Γ(m)))∫_0 ^∞ ((D^(m−1) sin^n x)/x)dx n+m∈Odd Number.

$$\mathrm{Prove}\:::\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}^{\mathrm{m}} }\mathrm{dx}=\frac{\mathrm{1}}{\Gamma\left(\mathrm{m}\right)}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{D}^{\mathrm{m}−\mathrm{1}} \mathrm{sin}^{\mathrm{n}} \mathrm{x}}{\mathrm{x}}\mathrm{dx} \\ $$$$\mathrm{n}+\mathrm{m}\in\mathrm{Odd}\:\mathrm{Number}. \\ $$

Question Number 159925 Answers: 1 Comments: 0

Find out pairs of numbers (a,b) (as many as you can) such that: (√a) +(√b) , a+b , a^2 +b^2 ∈ P

$$\mathrm{Find}\:\mathrm{out}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{numbers}\:\left(\mathrm{a},\mathrm{b}\right)\:\left(\mathrm{as}\right. \\ $$$$\left.\mathrm{many}\:\mathrm{as}\:\mathrm{you}\:\mathrm{can}\right)\:\mathrm{such}\:\mathrm{that}: \\ $$$$\sqrt{\mathrm{a}}\:+\sqrt{\mathrm{b}}\:,\:\mathrm{a}+\mathrm{b}\:,\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:\in\:\mathbb{P} \\ $$

Question Number 159921 Answers: 0 Comments: 0

Question Number 159918 Answers: 0 Comments: 2

y = sin 8x cos 4x y^((n)) =?

$$\:\:{y}\:=\:\mathrm{sin}\:\mathrm{8}{x}\:\mathrm{cos}\:\mathrm{4}{x}\: \\ $$$$\:\:{y}^{\left({n}\right)} \:=? \\ $$

Question Number 159917 Answers: 0 Comments: 1

Question Number 159915 Answers: 0 Comments: 1

∫_1 ^(16) ((√x)/(1+(x^3 )^(1/4) )) dx =?

$$\:\:\int_{\mathrm{1}} ^{\mathrm{16}} \:\frac{\sqrt{{x}}}{\mathrm{1}+\sqrt[{\mathrm{4}}]{{x}^{\mathrm{3}} }}\:{dx}\:=? \\ $$

Question Number 159928 Answers: 1 Comments: 0

$$ \\ $$$$ \\ $$

Question Number 159911 Answers: 1 Comments: 0

Question Number 159906 Answers: 1 Comments: 0

lim_(x→0) ((tan tan tan ...tan x_(n) −sin sin sin ...sin x_(n) )/x^2 )=?

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{n}} {\underbrace{\mathrm{tan}\:\mathrm{tan}\:\mathrm{tan}\:...\mathrm{tan}\:\mathrm{x}}}−\underset{\mathrm{n}} {\underbrace{\mathrm{sin}\:\mathrm{sin}\:\mathrm{sin}\:...\mathrm{sin}\:\mathrm{x}}}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$

Question Number 159891 Answers: 1 Comments: 0

S=Σ_(k=1) ^(2002 ) (√(((k^2 +1)/k^2 )+(1/((k+1)^2 )))) =?

$$\:\:\:\:{S}=\underset{{k}=\mathrm{1}} {\overset{\mathrm{2002}\:} {\sum}}\sqrt{\frac{{k}^{\mathrm{2}} +\mathrm{1}}{{k}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({k}+\mathrm{1}\right)^{\mathrm{2}} }}\:=? \\ $$

Question Number 159881 Answers: 0 Comments: 0

Resolve 1. u_n −3u_(n−1) =12((3/4))^n 2. u_n =2u_(n−1) +5cos (((nΠ)/3)), u_o =1 3. u_n =u_(n−1) −u_(n−2) +2sin (((nΠ)/3)) with u_o =1, u_1 =2

$${Resolve}\: \\ $$$$\mathrm{1}.\:\:{u}_{{n}} −\mathrm{3}{u}_{{n}−\mathrm{1}} =\mathrm{12}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{{n}} \\ $$$$\mathrm{2}.\:{u}_{{n}} =\mathrm{2}{u}_{{n}−\mathrm{1}} +\mathrm{5cos}\:\left(\frac{{n}\Pi}{\mathrm{3}}\right),\:{u}_{{o}} =\mathrm{1}\: \\ $$$$\mathrm{3}.\:{u}_{{n}} ={u}_{{n}−\mathrm{1}} −{u}_{{n}−\mathrm{2}} +\mathrm{2sin}\:\left(\frac{{n}\Pi}{\mathrm{3}}\right) \\ $$$${with}\:{u}_{{o}} =\mathrm{1},\:{u}_{\mathrm{1}} =\mathrm{2} \\ $$

Question Number 159874 Answers: 0 Comments: 3

Given the curve y=x^4 +3x^3 −6x^2 −3x determine for which value of α the tangent to the curve from point P(α,0) is maximum.

$$\:\:\:\:{Given}\:{the}\:{curve}\:{y}={x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} −\mathrm{3}{x} \\ $$$$\:{determine}\:{for}\:{which}\:{value}\: \\ $$$$\:{of}\:\alpha\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$$\:{from}\:{point}\:{P}\left(\alpha,\mathrm{0}\right)\:{is}\:{maximum}. \\ $$

Question Number 159873 Answers: 1 Comments: 0

j′ai besoin de la version pc de cette application et je veux savoir ci cest possible de transformer les documents .med en .pdf

$${j}'{ai}\:{b}\boldsymbol{{esoin}}\:\boldsymbol{{de}}\:\boldsymbol{{la}}\:\boldsymbol{{version}}\:\boldsymbol{{pc}}\:\boldsymbol{{de}}\:\boldsymbol{{cette}}\:\boldsymbol{{application}} \\ $$$$\boldsymbol{{et}}\:\boldsymbol{{je}}\:\boldsymbol{{veux}}\:\boldsymbol{{savoir}}\:\boldsymbol{{ci}}\:\boldsymbol{{cest}}\:\boldsymbol{{possible}}\:\boldsymbol{{de}}\:\boldsymbol{{transformer}}\:\boldsymbol{{les}}\:\boldsymbol{{documents}}\:.\boldsymbol{{med}}\:\boldsymbol{{en}}\:.\boldsymbol{{pdf}} \\ $$$$ \\ $$

Question Number 159870 Answers: 1 Comments: 0

∫ ((1−cot^2 x)/(1+sin x)) dx =?

$$\:\:\int\:\frac{\mathrm{1}−\mathrm{cot}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$

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

Contact: info@tinkutara.com