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Question Number 96558 Answers: 1 Comments: 0

Let m and n be two positive integers satisfy (m/n) = (1/(10×12))+(1/(12×14))+(1/(14×16))+...+(1/(2012×2014)) find the smallest possible value of m+n

$Let m and n be two positive integers$ $satisfy \frac{m}{n} = \frac{1}{10 \times 12} + \frac{1}{12 \times 14} + \frac{1}{14 \times 16} + . . . + \frac{1}{2012 \times 2014}$ $find the smallest possible value of$ $m + n$

Question Number 96554 Answers: 1 Comments: 2

∫(dx/(x!))=?

$\int \frac{dx}{x!} = ?$

Question Number 96548 Answers: 0 Comments: 1

Question Number 96543 Answers: 1 Comments: 0

Question Number 96542 Answers: 0 Comments: 6

Question Number 96538 Answers: 1 Comments: 0

Question Number 96530 Answers: 0 Comments: 1

If: (1+m)^3 −3m^3 =2 0≤m≤1 Find: (1+m)^2 −3m^2

$If : {(1 + m)}^{3} - 3 m^{3} = 2 0 ⩽ m ⩽ 1$ $Find : {(1 + m)}^{2} - 3 m^{2}$

Question Number 96527 Answers: 2 Comments: 1

proof that 1^2 +2^2 +3^2 +....+n^2 =((n(2n+1)(n+1))/6)

$proof that 1^{2} + 2^{2} + 3^{2} + . . . . + n^{2} = \frac{n (2 n + 1) (n + 1)}{6}$

Question Number 96524 Answers: 0 Comments: 1

∫(sinx^(cosx^(sinx) ) −cosx^(sinx^(cosx) ) )dx

$\int ({sinx}^{{cosx}^{sinx}} - {cosx}^{{sinx}^{cosx}}) dx$

Question Number 96523 Answers: 0 Comments: 0

Question Number 96514 Answers: 1 Comments: 3

∫_0 ^1 (1/(1+[(1/x)]))dx=?

$\underset{0}{\int^{1}} \frac{1}{1 + [\frac{1}{x}]} d x = ?$

Question Number 96508 Answers: 1 Comments: 0

Question Number 96505 Answers: 2 Comments: 2

((√((8)^(1/(4 )) −(√((√2)+1))))/((√((8)^(1/(4 )) +(√((√2)−1))))−(√((8)^(1/(4 )) −(√((√2)−1)))))) ?

$\frac{\sqrt{\sqrt[4]{8} - \sqrt{\sqrt{2} + 1}}}{\sqrt{\sqrt[4]{8} + \sqrt{\sqrt{2} - 1}} - \sqrt{\sqrt[4]{8} - \sqrt{\sqrt{2} - 1}}} ?$

Question Number 96500 Answers: 2 Comments: 0

If x and y real number satisfy (x+5)^2 +(y−12)^2 =196 , then the minimum value of x^2 +y^2 is

$If x a n d y r e a l n u m b e r s a t i s f y$ ${(x + 5)}^{2} + {(y - 12)}^{2} = 196, then$ $the minimum value of x^{2} + y^{2} i s$

Question Number 96495 Answers: 2 Comments: 0

calculateI = ∫_0 ^(π/2) ln(cosx +sinx)dx and J =∫_0 ^(π/2) ln(cosx−sinx)dx

$calculateI = \int_{0}^{\frac{π}{2}} \ln (cosx + sinx) dx$ $and J = \int_{0}^{\frac{π}{2}} \ln (cosx - sinx) dx$

Question Number 96489 Answers: 1 Comments: 0

Given { ((u_0 =a)),((u_(n+1) =a+(1/2)(1−(1/b^n ))u_n )) :} a>0 b>1 a\ Calculate u_1 , u_2 , and u_3 . b\ Show that the sequence (u_n )_(n∈N) is increasing. c\ Deduce that (u_n )_(n∈N) converges and determine its limit.

$G iven {\begin{cases} u_{0} = a \\ u_{n + 1} = a + \frac{1}{2} (1 - \frac{1}{b^{n}}) u_{n} \end{cases} a > 0 b > 1$ $a ∖ C alculate u_{1}, u_{2}, and u_{3} .$ $b ∖ S how that the sequence {(u_{n})}_{n \in N} is increasing .$ $c ∖ D educe that {(u_{n})}_{n \in N} converges and determine its limit .$

Question Number 96481 Answers: 0 Comments: 5

∫(1/dx)=?

$\int \frac{1}{dx} = ?$

Question Number 96479 Answers: 1 Comments: 0

show that ∫_1 ^e ((x−xln(x)+1)/(x(x+1)^2 +x ln^2 (x)))dx=arctan((1/(e+1)))

$s h o w t h a t$ $\int_{1}^{e} \frac{x - x l n (x) + 1}{x {(x + 1)}^{2} + x {l n}^{2} (x)} d x = a r c t a n (\frac{1}{e + 1})$

Question Number 96467 Answers: 1 Comments: 0

Suppose y = 8 ; (dy/dx) = 4 & (d^2 y/dx^2 ) ∣_(x=1) = −2 . Find the value of (1) ((d(xy))/dx) ∣_(x=1) (1)((d^2 (xy))/dx^2 ) ∣_(x=1)

$Suppose y = 8; \frac{d y}{d x} = 4 &$ $\frac{d^{2} y}{{d x}^{2}} ∣_{x = 1} = - 2 . Find the value$ $of (1) \frac{d (x y)}{d x} ∣_{x = 1}$ $(1) \frac{d^{2} (x y)}{{d x}^{2}} ∣_{x = 1}$

Question Number 96466 Answers: 0 Comments: 0

Question Number 96460 Answers: 1 Comments: 8

Question Number 96454 Answers: 1 Comments: 0

Question Number 96441 Answers: 1 Comments: 1

Question Number 96437 Answers: 1 Comments: 0

Question Number 96436 Answers: 0 Comments: 0

∮ x^2 dx = ???

$\oint x^{2} d x = ? ? ?$

Question Number 96429 Answers: 1 Comments: 0

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