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Question Number 175620 Answers: 0 Comments: 1

the domain of f(x) = (√(log_x {x})) ; {.} denote the fractional part is

$t h e d o m a i n o f f (x) = \sqrt{\log_{x} {x}};$ ${.} d e n o t e t h e f r a c t i o n a l p a r t i s$

Question Number 175618 Answers: 1 Comments: 2

Question Number 175614 Answers: 1 Comments: 0

∫(1/(4t^3 +3t^2 +4t+1))dt

$\int \frac{1}{4 t^{3} + 3 t^{2} + 4 t + 1} d t$

Question Number 175608 Answers: 1 Comments: 3

Question Number 175602 Answers: 1 Comments: 2

∫ (dx/(csc x+ cos x)) =?

$\int \frac{dx}{\csc x + \cos x} = ?$

Question Number 175601 Answers: 2 Comments: 0

Question Number 175623 Answers: 1 Comments: 0

min f(x)=(√(x^2 −2x+5)) +(√(4x^2 −4x+10))

$\min f (x) = \sqrt{x^{2} - 2 x + 5} + \sqrt{{4 x}^{2} - 4 x + 10}$

Question Number 175624 Answers: 3 Comments: 0

let p(x) = x^6 +ax^5 +bx^4 +cx^3 +dx^2 +ex+f be a polynomial function such that p(1) = 1 ; p(2) = 2 ; p(3) = 3 p(4) = 4 ; p(5) = 5 ; p(6) = 6 then find p(7) = ?

$let p (x) = x^{6} + {ax}^{5} + {bx}^{4} + {cx}^{3} + {dx}^{2} + ex + f$ $be a polynomial function such$ $that p (1) = 1; p (2) = 2; p (3) = 3$ $p (4) = 4; p (5) = 5; p (6) = 6 then$ $find p (7) = ?$

Question Number 175595 Answers: 0 Comments: 0

Question Number 175593 Answers: 0 Comments: 3

If 0<a≤b then prove that: determinant ((1,a,(log(a^a ))),(1,((√((a^2 +b^2 )/2)) (√((a^2 +b^2 )/8)) ∙ log(((a^2 +b^2 )/2))),),(1,b,(log(b^b ))))≥ 0

$If 0 < a ⩽ b then prove that :$ $| \begin{matrix} 1 & a & \log (a^{a}) \\ 1 & \sqrt{\frac{a^{2} + b^{2}}{2}} \sqrt{\frac{a^{2} + b^{2}}{8}} \cdot \log (\frac{a^{2} + b^{2}}{2}) \\ 1 & b & \log (b^{b}) \end{matrix} | ⩾ 0$

Question Number 175588 Answers: 2 Comments: 1

Question Number 175585 Answers: 1 Comments: 6

in AB^Δ C prove that: sin ((( A)/2) ) ≤ (( a)/( b + c)) ■

$i n A \overset{Δ}{B C} p r o v e t h a t :$ $s i n (\frac{A}{2}) ⩽ \frac{a}{b + c} ◼$

Question Number 175583 Answers: 0 Comments: 1

∫_0 ^2 x^t dt=3 solve for x

$\int_{0}^{2} x^{t} d t = 3$ $s o l v e f o r x$

Question Number 175579 Answers: 0 Comments: 0

lim_(x→∞) ((x^(1−sin ((1/x))) .(x^(sin ((1/x))) −1))/(ln x))

$\lim_{x \to \infty} \frac{x^{1 - \sin (\frac{1}{x})} . (x^{\sin (\frac{1}{x})} - 1)}{\ln x}$

Question Number 175573 Answers: 0 Comments: 0

Question Number 175572 Answers: 0 Comments: 0

Question Number 175571 Answers: 2 Comments: 0

Question Number 175567 Answers: 0 Comments: 0

in how many ways can you put 40 identical balls into 20 identical boxes such that each box obtains at least one ball and at most 5 balls?

$i n h o w m a n y w a y s c a n y o u p u t 40$ $i d e n t i c a l b a l l s i n t o 20 i d e n t i c a l b o x e s$ $s u c h t h a t e a c h b o x o b t a i n s a t l e a s t o n e$ $b a l l a n d a t m o s t 5 b a l l s ?$

Question Number 175568 Answers: 1 Comments: 1

Question Number 175554 Answers: 2 Comments: 0

x^(√x) =(√x^x ) find x

$x^{\sqrt{x}} = \sqrt{x^{x}}$ $f i n d x$

Question Number 175553 Answers: 1 Comments: 0

Question Number 175548 Answers: 1 Comments: 4

determinant ((( determinant (((2+424+44244+4442444+∙∙∙n terms=?_ ^ _() ^() )))_ ^ ^(∣•∣_(−) ^(−) ) )))

$\begin{matrix} \overset{\underline{\overset{―}{∣ ∙ ∣}}}{{\begin{matrix} \underset{}{\overset{}{2 + 424 + 44244 + 4442444 + \cdot \cdot \cdot n t e r m s = ?_{}^{}}} \end{matrix}}_{}^{}} \end{matrix}$

Question Number 175547 Answers: 2 Comments: 0

Question Number 175544 Answers: 1 Comments: 1

tan^6 (10°)+tan^6 (50°)+tan^6 (70°)=?

$\tan^{6} (10 °) + \tan^{6} (50 °) + \tan^{6} (70 °) = ?$

Question Number 175531 Answers: 2 Comments: 0

∫ (dt/(5cos t+6sin t)) =?

$\int \frac{d t}{5 \cos t + 6 \sin t} = ?$

Question Number 175511 Answers: 0 Comments: 1

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