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Question Number 161323 Answers: 1 Comments: 3

prove ((( −n )),(( k)) ) =^? (−1)^( k) ((( n +k −1)),(( k)) ) example : ((( −5)),(( 4)) ) = ((( 8)),(( 4)) )

$p r o v e$ $(\begin{matrix} - n \\ k \end{matrix}) \overset{?}{=} {(- 1)}^{k} (\begin{matrix} n + k - 1 \\ k \end{matrix})$ $e x a m p l e : (\begin{matrix} - 5 \\ 4 \end{matrix}) = (\begin{matrix} 8 \\ 4 \end{matrix})$

Question Number 161322 Answers: 1 Comments: 4

Question Number 161316 Answers: 1 Comments: 0

Three quarters of a number added to two and a half of that number gives 13. find the number

$Three quarters of a number added to$ $two and a half of that number gives$ $13 . find the number$

Question Number 161311 Answers: 2 Comments: 0

Differentiate y=sin xy

$D i f f e r e n t i a t e y = \sin x y$

Question Number 161296 Answers: 1 Comments: 0

Question Number 161295 Answers: 0 Comments: 2

prove that:x^8 +x^6 −x^3 −x+1>0,x∈R

$p r o v e t h a t : x^{8} + x^{6} - x^{3} - x + 1 > 0, x \in R$

Question Number 161294 Answers: 1 Comments: 0

∫_(−2) ^2 (x^3 cos((x/2))+(1/2))(√(4−x^2 ))dx

$\int_{- 2}^{2} (x^{3} \cos (\frac{x}{2}) + \frac{1}{2}) \sqrt{4 - x^{2}} dx$

Question Number 161285 Answers: 5 Comments: 0

(1) ∫ (dx/(1−2cos x)) (2) ∫ ((sin 2x)/(sin x−sin^2 2x)) dx (3) ∫ (dx/(cos 2x−sin x))

$(1) \int \frac{d x}{1 - 2 \cos x}$ $(2) \int \frac{\sin 2 x}{\sin x - \sin^{2} 2 x} d x$ $(3) \int \frac{d x}{\cos 2 x - \sin x}$

Question Number 161284 Answers: 0 Comments: 0

Question Number 161319 Answers: 1 Comments: 0

lim_(x→(π/2)) ((cos x)/( ((sin x+cos x))^(1/3) −sin x))=?

$\lim_{x \to \frac{π}{2}} \frac{\cos x}{\sqrt[3]{\sin x + \cos x} - \sin x} = ?$

Question Number 161282 Answers: 1 Comments: 0

Question Number 161281 Answers: 0 Comments: 0

Question Number 161280 Answers: 1 Comments: 0

if x;y;z>0 and (1/(1+x)) + (1/(1+y)) + (1/(1+z)) = 1 then prove that: x + y + z ≥ (3/4) xyz

$if x; y; z > 0 and \frac{1}{1 + x} + \frac{1}{1 + y} + \frac{1}{1 + z} = 1$ $then prove that :$ $x + y + z ⩾ \frac{3}{4} xyz$

Question Number 161272 Answers: 0 Comments: 0

Solve the differential systeme (Σ) below: (Σ) { ((x^. (t)=x(t)+2y(t)+t)),((y^. (t)=−4x(t)−3y(t))) :}

$Solve the differential systeme (Σ) below :$ $(Σ) {\begin{cases} \dot{x} (t) = x (t) + 2 y (t) + t \\ \dot{y} (t) = - 4 x (t) - 3 y (t) \end{cases}$

Question Number 161265 Answers: 1 Comments: 2

Question Number 161257 Answers: 2 Comments: 1

Question Number 161256 Answers: 1 Comments: 0

Given f(x)=f(x+2), ∀x∈R If ∫_0 ^2 f(x)dx= p then ∫_0 ^(2020) f(x+2a)dx=? for a∈Z^+

$G i v e n f (x) = f (x + 2), \forall x \in R$ $I f \underset{0}{\int^{2}} f (x) d x = p t h e n \underset{0}{\int^{2020}} f (x + 2 a) d x = ?$ $f o r a \in Z^{+}$

Question Number 161254 Answers: 0 Comments: 1

((4sin (((2π)/7))+sec ((π/(14))))/(cot ((π/7))))=?

$\frac{4 \sin (\frac{2 π}{7}) + \sec (\frac{π}{14})}{\cot (\frac{π}{7})} = ?$

Question Number 161251 Answers: 0 Comments: 0

Question Number 161248 Answers: 1 Comments: 0

lim_(x→0) (((1+sin^3 x)^4 −(1+tan^3 x)^4 )/x^5 ) =?

$\lim_{x \to 0} \frac{{(1 + \sin^{3} x)}^{4} - {(1 + \tan^{3} x)}^{4}}{x^{5}} = ?$

Question Number 161242 Answers: 1 Comments: 0

x ; y ; z < 0 (x^3 /( (√(yz)))) = -3 ; (y^3 /( (√(xz)))) = -6 ; (z^3 /( (√(xy)))) = -8 find x∙y∙z = ?

$x; y; z < 0$ $\frac{x^{3}}{\sqrt{yz}} = - 3; \frac{y^{3}}{\sqrt{xz}} = - 6; \frac{z^{3}}{\sqrt{xy}} = - 8$ $find x \cdot y \cdot z = ?$

Question Number 161241 Answers: 2 Comments: 0

Question Number 161238 Answers: 0 Comments: 0

Question Number 161234 Answers: 0 Comments: 1

1:!x=? 2:!!x=? 3:x!!=? when X is odd 4:x!!=? when X is evan 5:x!!!=? when X is odd 6:x!!!=? when X is evan

$1 :! x = ?$ $2 :!! x = ?$ $3 : x!! = ? w h e n X i s o d d$ $4 : x!! = ? w h e n X i s e v a n$ $5 : x!!! = ? w h e n X i s o d d$ $6 : x!!! = ? w h e n X i s e v a n$

Question Number 161233 Answers: 0 Comments: 0

Question Number 161229 Answers: 1 Comments: 0

Given f(x)= { ((1−∣x∣ ; x≤1)),((∣x∣−1 ; x>1)) :} find ∫_(−3) ^( 8) [f(x−1)+f(x+1)] dx.

$G i v e n f (x) = {\begin{cases} 1 - ∣ x ∣; x ⩽ 1 \\ ∣ x ∣ - 1; x > 1 \end{cases}$ $f i n d \int_{- 3}^{8} [f (x - 1) + f (x + 1)] d x .$

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