Question and Answers Forum

AllQuestion and Answers: Page 1144

Question Number 99995 Answers: 0 Comments: 0

(√(1(√(3(√(5(√(7(√9)))))))))...∞

$$\sqrt{\mathrm{1}\sqrt{\mathrm{3}\sqrt{\mathrm{5}\sqrt{\mathrm{7}\sqrt{\mathrm{9}}}}}}...\infty \\ $$

Question Number 99994 Answers: 1 Comments: 0

1+(1/(16))+(1/(81))+(1/(256))+.....∞

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{16}}+\frac{\mathrm{1}}{\mathrm{81}}+\frac{\mathrm{1}}{\mathrm{256}}+.....\infty \\ $$

Question Number 99992 Answers: 2 Comments: 0

y(1+x^3 )dy−x^2 dx = 0 ; y(2)=3

$$\mathrm{y}\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\mathrm{dy}−\mathrm{x}^{\mathrm{2}} \mathrm{dx}\:=\:\mathrm{0}\:;\:\mathrm{y}\left(\mathrm{2}\right)=\mathrm{3}\: \\ $$

Question Number 99989 Answers: 2 Comments: 0

(D^2 −4D+4)y = xe^(2x)

$$\left(\mathrm{D}^{\mathrm{2}} −\mathrm{4D}+\mathrm{4}\right)\mathrm{y}\:=\:{xe}^{\mathrm{2}{x}} \\ $$

Question Number 99986 Answers: 1 Comments: 0

Explain Einstein′s theory of Gravitation and explain why photons don′t fit Newton′s model but Einstein′s.

$$\mathrm{Explain}\:\mathrm{Einstein}'\mathrm{s}\:\mathrm{theory}\:\mathrm{of}\:\mathrm{Gravitation}\: \\ $$$$\mathrm{and}\:\mathrm{explain}\:\mathrm{why}\:\mathrm{photons}\:\mathrm{don}'\mathrm{t}\:\mathrm{fit}\:\mathrm{Newton}'\mathrm{s} \\ $$$$\mathrm{model}\:\mathrm{but}\:\mathrm{Einstein}'\mathrm{s}. \\ $$

Question Number 99985 Answers: 0 Comments: 0

A certain wire has length 4.5 cm and mass 12.3 g, with an electrical resistance of 1.1 mΩ. this wire falls through a horizontal magnetic field with flux density of 0.35 T. As his wire falls its ends slide smoothly between two rails connected by a wire with negligible internal resistance. Calculate the magnitude of the terminal energy resistance, neglecting the resistance of the rails.

$$\mathrm{A}\:\mathrm{certain}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{length}\:\mathrm{4}.\mathrm{5}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{mass}\:\mathrm{12}.\mathrm{3}\:\mathrm{g},\:\:\mathrm{with}\:\mathrm{an} \\ $$$$\mathrm{electrical}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{1}.\mathrm{1}\:\mathrm{m}\Omega.\:\mathrm{this}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{through}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{magnetic}\:\mathrm{field}\:\:\mathrm{with}\:\mathrm{flux}\:\mathrm{density}\:\mathrm{of}\:\mathrm{0}.\mathrm{35}\:\mathrm{T}.\:\mathrm{As}\:\mathrm{his}\:\mathrm{wire}\:\mathrm{falls}\:\mathrm{its}\:\mathrm{ends} \\ $$$$\mathrm{slide}\:\mathrm{smoothly}\:\mathrm{between}\:\mathrm{two}\:\mathrm{rails}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{wire}\:\mathrm{with}\:\mathrm{negligible} \\ $$$$\mathrm{internal}\:\mathrm{resistance}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{energy} \\ $$$$\mathrm{resistance},\:\mathrm{neglecting}\:\mathrm{the}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rails}. \\ $$

Question Number 99982 Answers: 0 Comments: 2

Question Number 99980 Answers: 0 Comments: 6

New enhacement

$$\mathrm{New}\:\mathrm{enhacement} \\ $$

Question Number 99975 Answers: 1 Comments: 0

((1/2))^(((1/3))^((1/4)....∞) ) =?

$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\mathrm{4}}....\infty} } =? \\ $$

Question Number 99972 Answers: 0 Comments: 1

Question Number 99968 Answers: 0 Comments: 1

lim_(x→0^+ ) (sin x)^(1/(ln(x))) =?

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\mathrm{sin}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{x}\right)}} \:=?\: \\ $$

Question Number 99962 Answers: 1 Comments: 0

A particle Q moves in a plane and its polar coordinate (r,θ) are described by r = at^2 and θ = (1/3)t^4 find its speed at t = 2s

$$\mathrm{A}\:\mathrm{particle}\:{Q}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{its}\:\mathrm{polar}\:\mathrm{coordinate}\:\left({r},\theta\right) \\ $$$$\mathrm{are}\:\mathrm{described}\:\mathrm{by}\:{r}\:=\:{at}^{\mathrm{2}} \:\mathrm{and}\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{3}}{t}^{\mathrm{4}} \:\mathrm{find}\:\mathrm{its} \\ $$$$\mathrm{speed}\:\mathrm{at}\:{t}\:=\:\mathrm{2s} \\ $$

Question Number 99960 Answers: 2 Comments: 1

Given y(√x)+x(√y) = 2. find the value of (dy/dx) ∣_((1,1)) = ?

$$\mathrm{Given}\:\mathrm{y}\sqrt{\mathrm{x}}+\mathrm{x}\sqrt{\mathrm{y}}\:=\:\mathrm{2}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:\mid_{\left(\mathrm{1},\mathrm{1}\right)} \:=\:?\: \\ $$

Question Number 99951 Answers: 1 Comments: 1

lim_(x→−∞) x^2 (√(x^2 +4x)) + x^3 ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4x}}\:+\:\mathrm{x}^{\mathrm{3}} \:? \\ $$

Question Number 99947 Answers: 1 Comments: 2

lim_(x→∞) x(5^(1/x) −1) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}\right)\:=? \\ $$

Question Number 99941 Answers: 1 Comments: 0

Question Number 99938 Answers: 2 Comments: 2

lim_(x→1^+ ) (((√(x^2 −1))+(√x)−1)/(√(x−1))) ?

$$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}+\sqrt{\mathrm{x}}−\mathrm{1}}{\sqrt{\mathrm{x}−\mathrm{1}}}\:?\: \\ $$

Question Number 99936 Answers: 2 Comments: 3

lim_(x→0) (((1+x)^k −1)/x)=? help me

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{k}} −\mathrm{1}}{\mathrm{x}}=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$

Question Number 99935 Answers: 1 Comments: 4

lim_(x→0) (1/x^(ln(e^x −1)) )=? help me

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}} −\mathrm{1}\right)} }=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$

Question Number 100162 Answers: 1 Comments: 1

Question Number 99923 Answers: 0 Comments: 2

Eliminate arbitrary constant a and b from z = (x−a)^2 +(y−b)^2 to form the partial differential equation.

$$\mathrm{Eliminate}\:\mathrm{arbitrary}\:\mathrm{constant}\: \\ $$$${a}\:\mathrm{and}\:{b}\:\mathrm{from}\:\mathrm{z}\:=\:\left(\mathrm{x}−{a}\right)^{\mathrm{2}} +\left(\mathrm{y}−{b}\right)^{\mathrm{2}} \\ $$$$\mathrm{to}\:\mathrm{form}\:\mathrm{the}\:\mathrm{partial}\:\mathrm{differential} \\ $$$$\mathrm{equation}.\: \\ $$

Question Number 99920 Answers: 3 Comments: 0

calculate Π_(n=2) ^∞ ((n^3 −1)/(n^3 +1))

$$\mathrm{calculate}\:\prod_{\mathrm{n}=\mathrm{2}} ^{\infty} \frac{\mathrm{n}^{\mathrm{3}} −\mathrm{1}}{\mathrm{n}^{\mathrm{3}} +\mathrm{1}} \\ $$

Question Number 99919 Answers: 1 Comments: 0

f_n is fibonacci sequence 1) find lim_(n→+∞) (f_(n+1) /(fn)) 2)prove that Σ f_n is convergente

$$\mathrm{f}_{\mathrm{n}} \mathrm{is}\:\mathrm{fibonacci}\:\mathrm{sequence} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\frac{\mathrm{f}_{\mathrm{n}+\mathrm{1}} }{{fn}} \\ $$$$\left.\mathrm{2}\right){prove}\:{th}\mathrm{a}{t}\:\Sigma\:\mathrm{f}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{convergente} \\ $$

Question Number 99916 Answers: 1 Comments: 0

can anyone recommend a good textbook from which i can learn calculus..^

$$\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{anyone}}\:\boldsymbol{\mathrm{recommend}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{good}}\:\boldsymbol{\mathrm{textbook}} \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{can}}\:\boldsymbol{\mathrm{learn}}\:\boldsymbol{\mathrm{calculus}}.\hat {.} \\ $$

Question Number 99905 Answers: 0 Comments: 5

Question Number 99900 Answers: 0 Comments: 0

An insulated wire of diameter 1.22 mm carries a steady current of 5.4 A. The insulation material is 1.22 mm thick and has a? coeffiecient of thermal conductivity of 0.23 W/Km. the electrical resistivity of the material of the wire is 5.2 ×10^(−7) Ωm. find the temperature difference between the inner and outer surface of the insulated material when steady state is reached.

$$\mathrm{An}\:\mathrm{insulated}\:\mathrm{wire}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{1}.\mathrm{22}\:\mathrm{mm}\:\mathrm{carries}\:\mathrm{a}\:\mathrm{steady}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{5}.\mathrm{4}\:\mathrm{A}.\:\mathrm{The}\:\mathrm{insulation}\:\mathrm{material}\:\mathrm{is}\:\mathrm{1}.\mathrm{22}\:\mathrm{mm}\:\mathrm{thick}\:\mathrm{and}\:\mathrm{has}\:\mathrm{a}? \\ $$$$\mathrm{coeffiecient}\:\mathrm{of}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{23}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{electrical} \\ $$$$\mathrm{resistivity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{material}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{5}.\mathrm{2}\:×\mathrm{10}^{−\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{temperature}\:\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{inner}\:\mathrm{and}\:\mathrm{outer}\:\mathrm{surface}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{insulated}\:\mathrm{material}\:\mathrm{when}\:\mathrm{steady}\:\mathrm{state}\:\mathrm{is}\:\mathrm{reached}. \\ $$

Pg 1139 Pg 1140 Pg 1141 Pg 1142 Pg 1143 Pg 1144 Pg 1145 Pg 1146 Pg 1147 Pg 1148

Contact: info@tinkutara.com