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Question Number 54699 Answers: 2 Comments: 3

∫ e^(2x) ((1/x) −(1/(2x^2 )))dx ∫e^(2x) (((1+sin 2x)/(1+cos 2x)))dx. Solve above Questions by using the formulae : ∫e^(kx) {f(kx)+f ′(kx)}dx= e^(kx) f(kx)+c.

$\int e^{2 x} (\frac{1}{x} - \frac{1}{2 x^{2}}) d x$ $\int e^{2 x} (\frac{1 + \sin 2 x}{1 + \cos 2 x}) d x .$ $S o l v e a b o v e Q u e s t i o n s b y u s i n g t h e$ $f o r m u l a e :$ $\int e^{k x} {f (k x) + f^{'} (k x)} d x = e^{k x} f (k x) + c .$

Question Number 54698 Answers: 2 Comments: 0

How many words with at least 2 letters can be formed using the letters from TINKUTARA?

$H o w m a n y w o r d s w i t h a t l e a s t 2 l e t t e r s$ $c a n b e f o r m e d u s i n g t h e l e t t e r s f r o m$ $T I N K U T A R A ?$

Question Number 54679 Answers: 2 Comments: 1

Question Number 54675 Answers: 1 Comments: 1

simplify A_n =Σ_(k=0) ^n k^2 C_n ^k cos(kθ) and B_n =Σ_(k=0) ^n k^2 C_n ^k sin(kθ) .

$s i m p l i f y A_{n} = \sum_{k = 0}^{n} k^{2} C_{n}^{k} c o s (k θ) a n d B_{n} = \sum_{k = 0}^{n} k^{2} C_{n}^{k} s i n (k θ) .$

Question Number 54688 Answers: 1 Comments: 1

f(x)=((2[x])/(3x−[x])) examine its continuity at x=((−1)/2) where [x] is greatest integer function

$f (x) = \frac{2 [x]}{3 x - [x]} e x a m i n e i t s c o n t i n u i t y a t x = \frac{- 1}{2}$ $w h e r e [x] i s g r e a t e s t i n t e g e r f u n c t i o n$

Question Number 54663 Answers: 1 Comments: 1

y = cos2t×sen2t y′ = ?

$y = c o s 2 t \times s e n 2 t$ $y^{'} = ?$

Question Number 54661 Answers: 1 Comments: 3

Question Number 54659 Answers: 1 Comments: 2

Question Number 54658 Answers: 0 Comments: 0

Question Number 54647 Answers: 0 Comments: 3

show that a. Σ_(r=1) ^(n) r^3 ._n C_r =n^2 (n+3).2^(n−3) b. _n C_0 ._n C_1 +_n C_1 ._n C_2 +...+_n C_(n−1) ._n C_n =(((2n)!)/((n−1)!.(n+1)!))

$show that$ $a . \underset{r = 1}{\overset{n}{Σ}} r^{3} ._{n} C_{r} = n^{2} (n + 3) . 2^{n - 3}$ $b ._{n} C_{0} ._{n} C_{1} +_{n} C_{1} ._{n} C_{2} + . . . +_{n} C_{n - 1} ._{n} C_{n} = \frac{(2 n)!}{(n - 1)! . (n + 1)!}$

Question Number 54646 Answers: 2 Comments: 0

Such That a. _(n+1) C_r =(((n+1). _n C_r )/((n−r+1))) b. _n C_0 +_n C_2 +_n C_(4...) =_n C_1 +_n C_3 +_n C_(5...) =2^(n−1)

$Such That$ $a ._{n + 1} C_{r} = \frac{(n + 1) ._{n} C_{r}}{(n - r + 1)}$ $b ._{n} C_{0} +_{n} C_{2} +_{n} C_{4 . . .} =_{n} C_{1} +_{n} C_{3} +_{n} C_{5 . . .} = 2^{n - 1}$

Question Number 54644 Answers: 1 Comments: 0

A= [(3,7),((−1),(−2)) ] A^(27) +A^(31) +A^(40) =...

$A = [\begin{matrix} 3 & 7 \\ - 1 & - 2 \end{matrix}]$ $A^{27} + A^{31} + A^{40} = . . .$

Question Number 54641 Answers: 0 Comments: 1

Given f(x) = ((4x + (√(4x^2 − 1)))/((√(2x + 1)) − (√(2x − 1)))) Find the value of f(13) + f(14) + f(15) + ... + f(112)

$Given$ $f (x) = \frac{4 x + \sqrt{4 x^{2} - 1}}{\sqrt{2 x + 1} - \sqrt{2 x - 1}}$ $Find the value of$ $f (13) + f (14) + f (15) + . . . + f (112)$

Question Number 54626 Answers: 2 Comments: 0

((1+sinx+cox)/(1+sinx−cosx))=((1−cosx)/(1+cosx))

$\frac{1 + sinx + cox}{1 + sinx - cosx} = \frac{1 - cosx}{1 + cosx}$

Question Number 54616 Answers: 2 Comments: 0

Question Number 54607 Answers: 1 Comments: 2

If ((u^5 +v^5 )/((u+v)^5 )) = −(1/5) , find ((u^3 +v^3 )/((u+v)^3 )) = ?

$I f \frac{u^{5} + v^{5}}{{(u + v)}^{5}} = - \frac{1}{5},$ $f i n d \frac{u^{3} + v^{3}}{{(u + v)}^{3}} = ?$

Question Number 54603 Answers: 1 Comments: 0

a,b,c ,are nonnegative real numbers and: a+b+c=1 . show that: 0≤ ab+bc+ca−2abc ≤(7/(27)) .

$a, b, c, a r e n o n n e g a t i v e r e a l n u m b e r s$ $a n d : a + b + c = 1 .$ $s h o w t h a t :$ $0 ⩽ ab + bc + ca - 2 abc ⩽ \frac{7}{27} .$

Question Number 54602 Answers: 0 Comments: 1

in a given triangle: tg(C/2)=((a.tgA+b.tgB)/(a+b)) . define the kind of triangle.

$i n a g i v e n t r i a n g l e :$ $tg \frac{C}{2} = \frac{a . tgA + b . tgB}{a + b} .$ $define the kind of triangle .$

Question Number 54600 Answers: 2 Comments: 2

solve for: x 1) (√(3−x))+(√(x+1))>(1/2) 2) cos^2 x+cos^2 2x+cos^2 3x=1 3)(√(x^2 −p))+2(√(x^2 −1))=x [p∈R]

$solve for : x$ $1) \sqrt{3 - x} + \sqrt{x + 1} > \frac{1}{2}$ $2) \cos^{2} x + \cos^{2} 2 x + \cos^{2} 3 x = 1$ $3) \sqrt{x^{2} - p} + 2 \sqrt{x^{2} - 1} = x [p \in R]$

Question Number 54595 Answers: 0 Comments: 3

x+y=a z+bx=c bz+xy=d Find yz in terms of a,b,c,d.

$x + y = a$ $z + b x = c$ $b z + x y = d$ $F i n d y z i n t e r m s o f a, b, c, d .$

Question Number 54588 Answers: 1 Comments: 0

What is : (d/dx) [ u(x) × v(x) × w(x) ] = ... and more generally, what is : (d/dx) [ Π_(i=1) ^n u_i (x)] = ... Thank you

$What is :$ $\frac{d}{dx} [u (x) \times v (x) \times w (x)] = . . .$ $and more generally, what is :$ $\frac{d}{dx} [\underset{i = 1}{\prod^{n}} u_{i} (x)] = . . .$ $Thank you$

Question Number 54586 Answers: 1 Comments: 0

(√(1−x^2 )) + (√(1−y^2 )) = a(x−y) prove that (dy/dx)=(√((1−y^2 )/(1−x^2 )))

$\sqrt{1 - x^{2}} + \sqrt{1 - y^{2}} = a (x - y)$ $p r o v e t h a t$ $\frac{d y}{d x} = \sqrt{\frac{1 - y^{2}}{1 - x^{2}}}$

Question Number 54585 Answers: 1 Comments: 1

show that ∫_0 ^∞ (x/(1+x^6 ))dx=(π/(3(√3)))

$s h o w t h a t \int_{0}^{\infty} \frac{x}{1 + x^{6}} d x = \frac{π}{3 \sqrt{3}}$

Question Number 54584 Answers: 2 Comments: 0

Question Number 54582 Answers: 0 Comments: 1

Solve for x: (1/(√(x + (√x) + 1))) + (2/(√(x + (√x) − 2))) = (√(x + 1))

$Solve for x : \frac{1}{\sqrt{x + \sqrt{x} + 1}} + \frac{2}{\sqrt{x + \sqrt{x} - 2}} = \sqrt{x + 1}$

Question Number 54578 Answers: 1 Comments: 1

A particle of mass 1.5kg rests on a rough plane inclined at 45° to the horizontal. It is maintained in equilibrium by a horizontal force of p newtons. Given that the coefficient of friction between the particle and the plane is (1/4), calculate the value of p when the particle is on the point of moving i. down the plane ii. up the plane [take g=10ms^(−2) ].

$A particle of mass 1 . 5 kg rests on a rough$ $plane inclined at 45 ° to the horizontal .$ $It is maintained in equilibrium by a$ $horizontal force of p newtons . Given$ $that the coefficient of friction between$ $the particle and the plane is \frac{1}{4}, calculate$ $the value of p when the particle is on$ $the point of moving$ $i . down the plane$ $ii . up the plane$ $[take g = {10 ms}^{- 2}] .$

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