Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1185

Question Number 98368    Answers: 1   Comments: 0

If G^→ is the centroid of a △ABC, then GA^(→) +GB^(→) +GC^(→) =

$$\mathrm{If}\:\overset{\rightarrow} {{G}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{a}\:\bigtriangleup{ABC},\:\mathrm{then} \\ $$$$\overset{\rightarrow} {{GA}}+\overset{\rightarrow} {{GB}}+\overset{\rightarrow} {{GC}}\:= \\ $$

Question Number 98367    Answers: 1   Comments: 2

show that ϕ(x)=x^2 −x^(−1) is an explicit solution to linear equation (d^2 y/dx^2 ) − ((2y)/x^2 ) = 0

$$\mathrm{show}\:\mathrm{that}\:\varphi\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{x}^{−\mathrm{1}} \:\mathrm{is}\:\mathrm{an}\:\mathrm{explicit}\: \\ $$$$\mathrm{solution}\:\mathrm{to}\:\mathrm{linear}\:\mathrm{equation}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\:\frac{\mathrm{2y}}{\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{0} \\ $$

Question Number 98355    Answers: 1   Comments: 1

Question Number 98342    Answers: 1   Comments: 2

Question Number 98338    Answers: 2   Comments: 0

∫cos(x^(18) ) dx

$$\int{cos}\left({x}^{\mathrm{18}} \right)\:{dx} \\ $$$$ \\ $$

Question Number 98325    Answers: 1   Comments: 0

Find the curvature vector and its magnitude at any point r^→ = (θ) of the curve r^→ = (acos θ,asin θ,aθ) .Show the locus of the feet of the ⊥ from the origin to the tangent is a curve that completely lies on the hyperbolic x^2 +y^2 −z^2 = a^2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{curvature}\:\mathrm{vector}\:\mathrm{and} \\ $$$$\mathrm{its}\:\mathrm{magnitude}\:\mathrm{at}\:\mathrm{any}\:\mathrm{point}\: \\ $$$$\overset{\rightarrow} {\mathrm{r}}\:=\:\left(\theta\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\overset{\rightarrow} {\mathrm{r}}=\:\left(\mathrm{acos}\:\theta,\mathrm{asin}\:\theta,\mathrm{a}\theta\right) \\ $$$$.\mathrm{Show}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{feet}\:\mathrm{of}\:\mathrm{the} \\ $$$$\bot\:\mathrm{from}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{to}\:\mathrm{the}\:\mathrm{tangent}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{curve}\:\mathrm{that}\:\mathrm{completely}\:\mathrm{lies} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{hyperbolic}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} =\:\mathrm{a}^{\mathrm{2}} \\ $$

Question Number 98320    Answers: 1   Comments: 0

Question Number 98311    Answers: 1   Comments: 0

calculate ∫_0 ^∞ ((lnx)/((1+x)^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\mathrm{dx}\: \\ $$

Question Number 98310    Answers: 0   Comments: 0

prove by using serie that ∫_0 ^∞ cos(x^2 )dx =∫_0 ^∞ sin(x^2 )dx

$$\mathrm{prove}\:\mathrm{by}\:\mathrm{using}\:\mathrm{serie}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}\:=\int_{\mathrm{0}} ^{\infty} \mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$

Question Number 98309    Answers: 1   Comments: 0

let f(x) = ln( 1 + cosh 2x) show that lim_(x→∞) f(x) = 2x − ln 2 hence deduce lim_(x→−∞) f(x) with the asympotes of the curve.

$$\mathrm{let}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\:\mathrm{1}\:+\:\mathrm{cosh}\:\mathrm{2}{x}\right) \\ $$$$\mathrm{show}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\mathrm{2}{x}\:−\:\mathrm{ln}\:\mathrm{2} \\ $$$$\mathrm{hence}\:\mathrm{deduce}\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:\mathrm{with}\:\mathrm{the}\:\mathrm{asympotes}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{curve}. \\ $$

Question Number 98306    Answers: 2   Comments: 1

Question Number 98305    Answers: 2   Comments: 0

calculate ∫_0 ^∞ ((ln(x))/((1+x)^3 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{3}} }\mathrm{dx} \\ $$

Question Number 98280    Answers: 1   Comments: 0

Let {a_n } be a sequence such that a_1 = 2, a_(n + 1) = ((3a_n + 4)/(2a_n + 3)), n ≥ 1, find a_n

$$\boldsymbol{\mathrm{Let}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{be}}\:\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sequence}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\:\:\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:=\:\:\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:=\:\:\frac{\mathrm{3}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:+\:\:\mathrm{4}}{\mathrm{2}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:\:+\:\:\mathrm{3}},\:\:\:\:\:\boldsymbol{\mathrm{n}}\:\geqslant\:\mathrm{1},\:\:\:\:\:\boldsymbol{\mathrm{find}}\:\:\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \\ $$

Question Number 98278    Answers: 1   Comments: 0

Question Number 98275    Answers: 1   Comments: 1

Question Number 98270    Answers: 2   Comments: 0

prove Fg=G((m_1 m_2 )/r^2 )

$${prove} \\ $$$${Fg}={G}\frac{{m}_{\mathrm{1}} {m}_{\mathrm{2}} }{{r}^{\mathrm{2}} } \\ $$

Question Number 98271    Answers: 2   Comments: 5

GivenU_n =∫_0 ^1 x^n (√(1−x))dx n∈N, show that U_n =((2^(n+2) n!(n+1))/((2n+3)!))

$$\mathcal{G}\mathrm{ivenU}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{x}^{\mathrm{n}} \sqrt{\mathrm{1}−\mathrm{x}}\mathrm{dx}\:\:\mathrm{n}\in\mathbb{N},\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{U}_{\mathrm{n}} =\frac{\mathrm{2}^{\mathrm{n}+\mathrm{2}} \mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)}{\left(\mathrm{2n}+\mathrm{3}\right)!} \\ $$

Question Number 98268    Answers: 0   Comments: 7

let p(x) be a polynomial function of (n−1)^(th) degree and p(k)=k for k=1,2,3,...,n find p(0) and p(n+1). example: n=10

$${let}\:{p}\left({x}\right)\:{be}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$$\left({n}−\mathrm{1}\right)^{{th}} \:{degree}\:{and} \\ $$$${p}\left({k}\right)={k}\:{for}\:{k}=\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$$${find}\:{p}\left(\mathrm{0}\right)\:{and}\:{p}\left({n}+\mathrm{1}\right). \\ $$$${example}:\:{n}=\mathrm{10} \\ $$

Question Number 98267    Answers: 2   Comments: 0

∀ a,b>0 , a^2 +b^2 =1 prove that ((1/a)+(1/b))((b/(a^2 +1))+(a/(b^2 +1)))≥(8/3)

$$\forall\:{a},{b}>\mathrm{0}\:,\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\left(\frac{{b}}{{a}^{\mathrm{2}} +\mathrm{1}}+\frac{{a}}{{b}^{\mathrm{2}} +\mathrm{1}}\right)\geqslant\frac{\mathrm{8}}{\mathrm{3}} \\ $$

Question Number 98259    Answers: 2   Comments: 4

Question Number 98256    Answers: 2   Comments: 0

∫_0 ^∞ ((log(x))/((√x)(x+1)^2 ))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{log}\left({x}\right)}{\sqrt{{x}}\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 98255    Answers: 1   Comments: 1

solve the following initial values DEs 20y′′ + 4y′ +y = 0 ; y(0) = 3.2 and y′(0) = 0

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{initial}\:\mathrm{values} \\ $$$$\mathrm{DEs}\:\mathrm{20y}''\:+\:\mathrm{4y}'\:+\mathrm{y}\:=\:\mathrm{0} \\ $$$$;\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{3}.\mathrm{2}\:\mathrm{and}\:\mathrm{y}'\left(\mathrm{0}\right)\:=\:\mathrm{0}\: \\ $$

Question Number 98250    Answers: 0   Comments: 1

Let A= (((2 2)),((1 3)) ) . Find a non singular matrix P such that P^(−1) AP is a diagonal matrix.

$$\mathrm{Let}\:\mathrm{A}=\begin{pmatrix}{\mathrm{2}\:\:\:\:\mathrm{2}}\\{\mathrm{1}\:\:\:\:\mathrm{3}}\end{pmatrix}\:.\:\mathrm{Find}\:\mathrm{a}\:\mathrm{non}\:\mathrm{singular}\:\mathrm{matrix} \\ $$$$\mathrm{P}\:\mathrm{such}\:\mathrm{that}\:\mathrm{P}^{−\mathrm{1}} \mathrm{AP}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diagonal}\:\mathrm{matrix}. \\ $$

Question Number 98249    Answers: 0   Comments: 0

explicit A(θ) =∫_1 ^(+∞) ((ln(lnx))/(x^2 +2xcosθ +1))dx with −π<θ<π

$$\mathrm{explicit}\:\mathrm{A}\left(\theta\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{ln}\left(\mathrm{lnx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{2xcos}\theta\:+\mathrm{1}}\mathrm{dx}\:\:\:\mathrm{with}\:−\pi<\theta<\pi \\ $$

Question Number 98248    Answers: 0   Comments: 0

find the value of ∫_1 ^(+∞) ((ln(lnx))/(x^2 +1))dx

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\mathrm{ln}\left(\mathrm{lnx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 98246    Answers: 1   Comments: 0

∫(x/(sin^2 (x−3)))dx

$$\int\frac{{x}}{{sin}^{\mathrm{2}} \left({x}−\mathrm{3}\right)}{dx} \\ $$

  Pg 1180      Pg 1181      Pg 1182      Pg 1183      Pg 1184      Pg 1185      Pg 1186      Pg 1187      Pg 1188      Pg 1189   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com