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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

Question Number 60424 Answers: 0 Comments: 2

let z ∈C and ∣z∣<1 find f(x)=∫_0 ^1 ln(1+zx)dx.

$${let}\:{z}\:\in{C}\:{and}\:\:\mid{z}\mid<\mathrm{1}\:\:{find} \\ $$$${f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{zx}\right){dx}. \\ $$

Question Number 60423 Answers: 1 Comments: 0

Question Number 60422 Answers: 1 Comments: 5

Question Number 60421 Answers: 1 Comments: 0

Question Number 60416 Answers: 0 Comments: 0

Sum the series: ^n C_0 ^n C_1 + ^n C_1 ^n C_2 + ^n C_2 ^n C_3 + ... + ^n C_r ^n C_(r + 1)

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{0}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{1}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{2}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{3}} \:+\:...\:+\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}} \overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{r}\:+\:\mathrm{1}} \\ $$

Question Number 60413 Answers: 1 Comments: 4

Question Number 60410 Answers: 0 Comments: 2

lim_(x→0) [(x^2 /(tanxsinx))] [.]=grestest integer function

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{{x}^{\mathrm{2}} }{{tanxsinx}}\right]\:\left[.\right]={grestest}\:{integer}\:{function} \\ $$

Question Number 60406 Answers: 1 Comments: 0

n ∈ Z^+ , Find the coefficient of x^(−1) in the expansion of (1 + x)^n (1 + (1/x))^n

$$\mathrm{n}\:\in\:\mathbb{Z}^{+} ,\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\:\mathrm{x}^{−\mathrm{1}} \:\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{1}\:+\:\mathrm{x}\right)^{\mathrm{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{n}} \\ $$

Question Number 60398 Answers: 0 Comments: 3

I am very sorry mr W sir for taking your valuable time thank you very much i got my mistake. I will work on my basics thank you and I am very sorry.

$${I}\:{am}\:{very}\:{sorry}\:{mr}\:{W}\:{sir}\:{for}\:{taking}\:{your}\: \\ $$$${valuable}\:{time} \\ $$$${thank}\:{you}\:{very}\:{much}\:{i}\:{got}\:{my}\:{mistake}. \\ $$$${I}\:{will}\:{work}\:{on}\:{my}\:{basics}\:{thank}\:{you} \\ $$$${and}\:{I}\:{am}\:{very}\:{sorry}. \\ $$

Question Number 60386 Answers: 1 Comments: 4

lim_(x→0) ((sin(πcos^2 x))/x^2 ) why it can not be solved this way lim_(x→0) ((sin(πcos^2 x))/x^2 ) =lim_(x→0) ((sin(πcos^2 x))/(πcos^2 x))×lim_(x→0) ((πcos^2 x)/x^2 ) =π × lim_(x→0) ((cos^2 x)/x^2 ) but it is not equal to π

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$${why}\:{it}\:{can}\:{not}\:{be}\:{solved}\:{this}\:{way} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} } \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{sin}\left(\pi{cos}^{\mathrm{2}} {x}\right)}{\pi{cos}^{\mathrm{2}} {x}}×\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\pi{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$$=\pi\:×\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{cos}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} } \\ $$$${but}\:{it}\:{is}\:{not}\:{equal}\:{to}\:\pi \\ $$

Question Number 60384 Answers: 0 Comments: 0

∫e^(coth^(−1) (x)) dx

$$\int{e}^{{coth}^{−\mathrm{1}} \left({x}\right)} \:{dx}\: \\ $$

Question Number 60376 Answers: 1 Comments: 2

Question Number 60370 Answers: 2 Comments: 0

Question Number 60367 Answers: 0 Comments: 6

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