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Question Number 60495 Answers: 0 Comments: 0

find the value of ∫_0 ^1 ((ln(x))/((1−x^2 )^2 ))dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}\right)}{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 60494 Answers: 1 Comments: 1

find ∫ (√((√(2+x^2 ))−x))dx

$${find}\:\int\:\sqrt{\sqrt{\mathrm{2}+{x}^{\mathrm{2}} }−{x}}{dx} \\ $$

Question Number 60493 Answers: 0 Comments: 0

let f(x)=(√(1+(√(1+x^2 )))) approximate f(x) by a polynome at v(0)

$${let}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$${approximate}\:{f}\left({x}\right)\:{by}\:{a}\:{polynome} \\ $$$${at}\:{v}\left(\mathrm{0}\right) \\ $$

Question Number 60484 Answers: 1 Comments: 2

If a + b + c = 4 then find a^3 + b^3 + c^(3 ) = ?

$${If}\:\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{4} \\ $$$$ \\ $$$${then}\:{find} \\ $$$${a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}\:} =\:? \\ $$

Question Number 60481 Answers: 0 Comments: 0

Question Number 60856 Answers: 0 Comments: 0

if 0<x<1,lim_(n→+∞) ((x^x^x^.^.^.^x }n)/(((x^x )^x )^(x...}n) ))=? (? can be expressed by x)

$${if}\:\:\mathrm{0}<{x}<\mathrm{1},\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\frac{\left.{x}^{{x}^{{x}^{.^{.^{.^{{x}} } } } } } \right\}{n}}{\left(\left({x}^{{x}} \right)^{{x}} \right)^{\left.{x}...\right\}{n}} }=? \\ $$$$\left(?\:{can}\:{be}\:{expressed}\:{by}\:{x}\right) \\ $$

Question Number 60477 Answers: 2 Comments: 0

Question Number 60475 Answers: 1 Comments: 0

Question Number 60461 Answers: 1 Comments: 0

Two cogged wheels, of which one has 16 cogs and other has 27, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

$$\mathrm{Two}\:\mathrm{cogged}\:\mathrm{wheels},\:\mathrm{of}\:\mathrm{which}\:\mathrm{one}\:\mathrm{has} \\ $$$$\mathrm{16}\:\mathrm{cogs}\:\mathrm{and}\:\mathrm{other}\:\mathrm{has}\:\mathrm{27},\:\mathrm{work}\:\mathrm{into}\: \\ $$$$\mathrm{each}\:\mathrm{other}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{latter}\:\mathrm{turns}\:\mathrm{80}\:\mathrm{times}\:\mathrm{in}\: \\ $$$$\mathrm{three}\:\mathrm{quarters}\:\mathrm{of}\:\mathrm{a}\:\mathrm{minute},\:\mathrm{how}\:\mathrm{often} \\ $$$$\mathrm{does}\:\mathrm{the}\:\mathrm{other}\:\mathrm{turn}\:\mathrm{in}\:\mathrm{8}\:\mathrm{seconds}? \\ $$

Question Number 60459 Answers: 0 Comments: 4

Question Number 60453 Answers: 0 Comments: 0

Question Number 60452 Answers: 1 Comments: 1

Question Number 60450 Answers: 0 Comments: 0

Question Number 60445 Answers: 2 Comments: 1

Question Number 60441 Answers: 1 Comments: 0

If a sum of money doubles itself in a time T, when compounded continuously, find the rate of interest, in terms of T.

$$\mathrm{If}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\:\mathrm{money}\:\mathrm{doubles}\:\mathrm{itself} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{time}\:\mathrm{T},\:\mathrm{when}\:\mathrm{compounded} \\ $$$$\mathrm{continuously},\:\mathrm{find}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of} \\ $$$$\mathrm{interest},\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{T}. \\ $$

Question Number 60426 Answers: 0 Comments: 2

the function is considered f(x,y)=e^(xy) +(x/y)+sen((2x+3y)π) Calcule: (∂f/∂x),(∂f/∂y),(∂^2 f/∂x^2 ),(∂^2 f/(∂x∂y)). f_x (0,1),f_y (2,−1), f_(xx) (0,1),f_(xy) (2,−1)

$${the}\:{function}\:{is}\:{considered}\: \\ $$$${f}\left({x},{y}\right)={e}^{{xy}} +\frac{{x}}{{y}}+{sen}\left(\left(\mathrm{2}{x}+\mathrm{3}{y}\right)\pi\right)\:{Calcule}: \\ $$$$\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} },\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}.\:\:\:{f}_{{x}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{y}} \left(\mathrm{2},−\mathrm{1}\right),\:{f}_{{xx}} \left(\mathrm{0},\mathrm{1}\right),{f}_{{xy}} \left(\mathrm{2},−\mathrm{1}\right) \\ $$

Question Number 60425 Answers: 0 Comments: 0