Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1129

Question Number 104390    Answers: 1   Comments: 0

Question Number 104394    Answers: 1   Comments: 0

Question Number 104388    Answers: 1   Comments: 0

∫(dx/(x^2 ((x^3 −1))^(1/3) ))

$$\int\frac{\mathrm{d}{x}}{{x}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −\mathrm{1}}} \\ $$

Question Number 104383    Answers: 1   Comments: 1

When f(x) is a differentiable function satisfying x∙f(x)=x^2 +∫_0 ^( x) (x−t)∙f ′(t)dt Find ⇒ f(1)

$$\mathrm{When}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\mathrm{satisfying}\:\:{x}\centerdot{f}\left({x}\right)={x}^{\mathrm{2}} +\int_{\mathrm{0}} ^{\:{x}} \left({x}−{t}\right)\centerdot{f}\:'\left({t}\right){dt} \\ $$$$\mathrm{Find}\:\Rightarrow\:{f}\left(\mathrm{1}\right) \\ $$

Question Number 104377    Answers: 1   Comments: 6

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 .... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{196}\:\:\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:....\:\left(\mathrm{iii}\right) \\ $$

Question Number 104371    Answers: 1   Comments: 0

Question Number 104370    Answers: 1   Comments: 0

Question Number 104369    Answers: 1   Comments: 0

Question Number 104368    Answers: 1   Comments: 0

CH_3 CH_2 −CH=CH_2 +HCl→ help me

$${CH}_{\mathrm{3}} {CH}_{\mathrm{2}} −{CH}={CH}_{\mathrm{2}} +{HCl}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104367    Answers: 1   Comments: 0

CH_3 −CH_2 −CH_2 −CH_2 Cl+KOH→ help me

$${CH}_{\mathrm{3}} −{CH}_{\mathrm{2}} −{CH}_{\mathrm{2}} −{CH}_{\mathrm{2}} {Cl}+{KOH}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104366    Answers: 0   Comments: 2

CH_3 −CH_2 −CHMgCl−CH_3 +H_2 O→ help me

$${CH}_{\mathrm{3}} −{CH}_{\mathrm{2}} −{CHMgCl}−{CH}_{\mathrm{3}} +{H}_{\mathrm{2}} {O}\rightarrow \\ $$$${help}\:{me} \\ $$

Question Number 104364    Answers: 2   Comments: 1

Question Number 104853    Answers: 0   Comments: 0

lim_(x→1) Li(x^2 )−Li(x)=ln2

$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{Li}\left({x}^{\mathrm{2}} \right)−{Li}\left({x}\right)={ln}\mathrm{2} \\ $$

Question Number 104359    Answers: 1   Comments: 0

solve this using Riemann sum f(x)=2x ; [0,4] for n=4

$${solve}\:{this}\:{using}\:{Riemann} \\ $$$${sum}\:{f}\left({x}\right)=\mathrm{2}{x}\:;\:\left[\mathrm{0},\mathrm{4}\right]\:{for}\:{n}=\mathrm{4} \\ $$

Question Number 104357    Answers: 2   Comments: 0

(x+y+1) (dy/dx) = 1

$$\left({x}+{y}+\mathrm{1}\right)\:\frac{{dy}}{{dx}}\:=\:\mathrm{1}\: \\ $$

Question Number 104852    Answers: 0   Comments: 0

if g∈C(R,R) and. ∫_0 ^1 g(x)dx=(1/3)+∫_0 ^1 g^2 (x^2 )dx then ∫_0 ^1 g(x)dx=(2/3) and ∫_0 ^1 g^2 (x)dx=(1/2)

$$\:\:{if}\:\:{g}\in{C}\left(\mathbb{R},\mathbb{R}\right)\:{and}.\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{g}\left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{3}}+\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}^{\mathrm{2}} \right){dx}\: \\ $$$${then}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}\left({x}\right){dx}=\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {g}^{\mathrm{2}} \left({x}\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$

Question Number 104851    Answers: 4   Comments: 0

∫ ((√(x^2 −9))/x^3 ) dx

$$\int\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$

Question Number 104850    Answers: 0   Comments: 0

Let E be a no empty set with card=n≥1 Find in term of n Σ_(A,B⊆E) Card(A−B)=Σ_(A,B⊆E) Card(A∩B)=(1/3)Σ_(A,B⊆E) Card (A∪B)=n4^(n−1)

$${Let}\:\:{E}\:{be}\:{a}\:{no}\:{empty}\:{set}\:{with}\:{card}={n}\geqslant\mathrm{1} \\ $$$$\:{Find}\:{in}\:{term}\:{of}\:\:{n}\:\:\:\:\:\:\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}−{B}\right)=\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}\cap{B}\right)=\frac{\mathrm{1}}{\mathrm{3}}\underset{{A},{B}\subseteq{E}} {\sum}{Card}\:\left({A}\cup{B}\right)={n}\mathrm{4}^{{n}−\mathrm{1}} \:\:\:\: \\ $$

Question Number 104350    Answers: 1   Comments: 0

lim_(△x→0) ((sin ((α+△x)^n )−sin (α^n ))/(cos ((α+△x)^n )sin (α+△x)−cos (α^n )sin (α)))

$$\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\left(\alpha+\bigtriangleup{x}\right)^{{n}} \right)−\mathrm{sin}\:\left(\alpha^{{n}} \right)}{\mathrm{cos}\:\left(\left(\alpha+\bigtriangleup{x}\right)^{{n}} \right)\mathrm{sin}\:\left(\alpha+\bigtriangleup{x}\right)−\mathrm{cos}\:\left(\alpha^{{n}} \right)\mathrm{sin}\:\left(\alpha\right)} \\ $$

Question Number 104348    Answers: 3   Comments: 0

lim_(x→0) (((arc tan (x)−arc sin (x))/(x(1−cos (x)))))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{arc}\:\mathrm{tan}\:\left({x}\right)−\mathrm{arc}\:\mathrm{sin}\:\left({x}\right)}{{x}\left(\mathrm{1}−\mathrm{cos}\:\left({x}\right)\right)}\right) \\ $$

Question Number 104342    Answers: 1   Comments: 0

solve x (d^2 y/dx^2 )−(dy/dx)−4x^3 y = 8x^3 sin(x^2 )

$${solve}\:{x}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\frac{{dy}}{{dx}}−\mathrm{4}{x}^{\mathrm{3}} {y}\:=\:\mathrm{8}{x}^{\mathrm{3}} \mathrm{sin}\left({x}^{\mathrm{2}} \right) \\ $$

Question Number 104339    Answers: 3   Comments: 1

Examine ∫_0 ^3 ((2x)/((1−x^2 )^(2/3) )) dx

$${Examine}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{\mathrm{2}{x}}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}/\mathrm{3}} }\:{dx} \\ $$

Question Number 104338    Answers: 0   Comments: 0

∫((tdt)/((1+t^3 )((1+t^3 ))^(1/3) ))

$$\int\frac{\mathrm{tdt}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right)\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{t}^{\mathrm{3}} }} \\ $$

Question Number 104326    Answers: 1   Comments: 2

Suppose you had x rupees. Your father gave you more 6 rupees. You gave y rupees to your brother. Now how many rupees you have? You will buy three shirts with the rupees that you have now. Write the cost of each shirt.

$$\boldsymbol{\mathrm{Suppose}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{Your}} \\ $$$$\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{gave}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{more}}\:\mathrm{6}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{You}} \\ $$$$\boldsymbol{\mathrm{gave}}\:\boldsymbol{{y}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{brother}}.\:\boldsymbol{\mathrm{Now}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}?\:\boldsymbol{\mathrm{You}}\:\boldsymbol{\mathrm{will}} \\ $$$$\boldsymbol{\mathrm{buy}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{shirts}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{now}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{cost}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{each}} \\ $$$$\boldsymbol{\mathrm{shirt}}. \\ $$

Question Number 104312    Answers: 1   Comments: 0

∫_0 ^(π/4) ((√(sin^2 θ+2))/(sinθ))dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\sqrt{\mathrm{sin}^{\mathrm{2}} \theta+\mathrm{2}}}{\mathrm{sin}\theta}\mathrm{d}\theta \\ $$

Question Number 104302    Answers: 3   Comments: 2

  Pg 1124      Pg 1125      Pg 1126      Pg 1127      Pg 1128      Pg 1129      Pg 1130      Pg 1131      Pg 1132      Pg 1133   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com