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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.

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

Question Number 99895 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (1/((3n+1)^3 ))=((13)/(27)) 𝛇(3) +((2𝛑^3 )/(81(√3)))

$$\:\:\:\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} }=\frac{\mathrm{13}}{\mathrm{27}}\:\boldsymbol{\zeta}\left(\mathrm{3}\right)\:+\frac{\mathrm{2}\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{81}\sqrt{\mathrm{3}}}\: \\ $$

Question Number 99894 Answers: 1 Comments: 0

Σ_(n≥0) (1/(n^2 +1)) = ?

$$\:\:\: \\ $$$$\underset{\boldsymbol{{n}}\geqslant\mathrm{0}} {\sum}\:\:\frac{\mathrm{1}}{\boldsymbol{{n}}^{\mathrm{2}} +\mathrm{1}}\:=\:? \\ $$

Question Number 99892 Answers: 0 Comments: 0

solve the equation xa^(1/x) +(1/x)a^x =2a Where a{−1,0,1}

$${solve}\:{the}\:{equation} \\ $$$${xa}^{\frac{\mathrm{1}}{{x}}} +\frac{\mathrm{1}}{{x}}{a}^{{x}} =\mathrm{2}{a} \\ $$$${Where}\:{a}\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\} \\ $$

Question Number 99889 Answers: 1 Comments: 0

1+(1/2)+(1/3)+(1/4)+(1/5)+(1/6)+(1/7)+.......∞{Find the sum}