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Question Number 161177 Answers: 1 Comments: 0

Question Number 161176 Answers: 0 Comments: 0

calculate Θ := Σ_(n=1) ^∞ (( (−1 )^( n−1) )/(n ( n + (1/3) ))) =? ■ m.n −−−−−−−−−−−−−

$c a l c u l a t e$ $Θ := \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n (n + \frac{1}{3})} = ? ◼ m . n$ $- - - - - - - - - - - - -$

Question Number 161169 Answers: 2 Comments: 0

if 9x^2 +(1/x^2 )=3 then 27x^3 +(1/x^3 )=?

$i f 9 x^{2} + \frac{1}{x^{2}} = 3$ $t h e n$ $27 x^{3} + \frac{1}{x^{3}} = ?$

Question Number 161168 Answers: 2 Comments: 1

Show that U_n =((4n−1)/(7n+3)) is convergent sequence.

$S h o w t h a t U_{n} = \frac{4 n - 1}{7 n + 3} i s c o n v e r g e n t$ $s e q u e n c e .$

Question Number 161166 Answers: 1 Comments: 0

If ^4 log (x+2y) +^4 log (x−2y) = 1 . Minimum value of ∣x∣ − ∣y∣ is ... ?

$I f^{4} \log (x + 2 y) +^{4} \log (x - 2 y) = 1 .$ $M i n i m u m v a l u e o f ∣ x ∣ - ∣ y ∣ i s . . . ?$

Question Number 161163 Answers: 1 Comments: 0

Question Number 161162 Answers: 0 Comments: 0

f :]0,+∞[→]0,+∞[ is convex function for n≥2 an integer , prove : (f(1)^(f(1)) f(2)^(f(2)) ...f(n)^(f(n)) )^(1/(f(1)+f(2)+...+f(n))) +(f(1)f(2)...f(n))^(1/n) ≤f(1)+f(n)

$f :] 0, + \infty [\to] 0, + \infty [i s c o n v e x f u n c t i o n$ $f o r n ⩾ 2 a n i n t e g e r, p r o v e :$ ${(f {(1)}^{f (1)} f {(2)}^{f (2)} . . . f {(n)}^{f (n)})}^{\frac{1}{f (1) + f (2) + . . . + f (n)}} + {(f (1) f (2) . . . f (n))}^{\frac{1}{n}} ⩽ f (1) + f (n)$

Question Number 161159 Answers: 2 Comments: 0

Question Number 161150 Answers: 0 Comments: 1

Question Number 161156 Answers: 1 Comments: 0

Calculate lim_(x→+∞) (ln (1+e^(−x) ))^(1/x) lim_(x→0) ((x/(2+sin (1/x)))) lim_(x→0) (((a^x +b^x )/2))^(1/x)

$C a l c u l a t e$ $\lim_{x \to + \infty} {(\ln (1 + e^{- x}))}^{\frac{1}{x}}$ $\lim_{x \to 0} (\frac{x}{2 + \sin \frac{1}{x}})$ $\lim_{x \to 0} {(\frac{a^{x} + b^{x}}{2})}^{\frac{1}{x}}$

Question Number 161146 Answers: 0 Comments: 0

Question Number 161147 Answers: 0 Comments: 0

Question Number 161139 Answers: 0 Comments: 0

Question Number 161136 Answers: 2 Comments: 0

≺ X , τ ≻ is a topological space and A ⊆ X , A^− =^? ∩_(F⊃A) F ( F is closed set )

$≺ X, τ ≻ i s a t o p o l o g i c a l s p a c e$ $a n d A \subseteq X,$ $\bar{A} \overset{?}{=} \underset{F \supset A}{\cap} F (F i s c l o s e d s e t)$

Question Number 161133 Answers: 1 Comments: 0

lim_(n→∞) (1/n)∫_0 ^1 (dx/(x(x+(1/n))))=?

$\lim_{n \to \infty} \frac{1}{n} \int_{0}^{1} \frac{dx}{x (x + \frac{1}{n})} = ?$

Question Number 161123 Answers: 0 Comments: 0

Find: 𝛀 =lim_(n→∞) (H_n /(n(H_(2n-1) - 2 H_(n-1) )))

$Find : Ω = \lim_{n \to \infty} \frac{H_{n}}{n (H_{2 n - 1} - 2 H_{n - 1})}$

Question Number 161130 Answers: 1 Comments: 0

Given P(x) is polynomial such that P(3x)= P ′(x).P ′′(x) . Find the tangent of curve y = P(x) parallel to the line y= 4x−2.

$G i v e n P (x) i s p o l y n o m i a l s u c h t h a t$ $P (3 x) = P^{'} (x) . P^{″} (x) . F i n d t h e t a n g e n t$ $o f c u r v e y = P (x) p a r a l l e l t o t h e l i n e$ $y = 4 x - 2 .$

Question Number 161126 Answers: 1 Comments: 2

Question Number 161111 Answers: 1 Comments: 1

lim_(x→0) ((x^2 +2cos x−2)/x^4 ) = (1/a) a=?

$\lim_{x \to 0} \frac{x^{2} + 2 \cos x - 2}{x^{4}} = \frac{1}{a}$ $a = ?$

Question Number 161105 Answers: 1 Comments: 1

Question Number 161102 Answers: 1 Comments: 1

Question Number 161101 Answers: 1 Comments: 0

solve: ∫((x+1)/(x^2 −7x−3))dx

$s o l v e :$ $\int \frac{x + 1}{x^{2} - 7 x - 3} d x$

Question Number 161100 Answers: 0 Comments: 0

f(x^2 )= 2+∫_( 0) ^( x^2 ) f(y) (1−tan y)dy , ∀x∈R f(−π)=?

$f (x^{2}) = 2 + \int_{0}^{x^{2}} f (y) (1 - \tan y) dy, \forall x \in R$ $f (- π) = ?$

Question Number 161096 Answers: 0 Comments: 0

if x;y;z>0 and a;b;c>0 different in pairs and n;k∈N^∗ ((log x^n )/(b^k - c^k )) = ((log y^n )/(c^k - a^k )) = ((log z^n )/(a^k - b^k )) then find (√(xyz))

$if x; y; z > 0 and a; b; c > 0$ $different in pairs and n; k \in N^{*}$ $\frac{\log x^{n}}{b^{k} - c^{k}} = \frac{\log y^{n}}{c^{k} - a^{k}} = \frac{\log z^{n}}{a^{k} - b^{k}}$ $then find \sqrt{xyz}$

Question Number 161091 Answers: 1 Comments: 0

Solve for real numbers: (√(1 - x)) = 2x^2 - 1 - 2x (√(1 - x^2 ))

$Solve for real numbers :$ $\sqrt{1 - x} = {2 x}^{2} - 1 - 2 x \sqrt{1 - x^{2}}$

Question Number 161114 Answers: 0 Comments: 0

Let f(x)= sin^3 (2x) for −(π/4)≤x≤(π/4) then Df^(−1) ((1/8))=(a/(b(√b))) so { ((a=?)),((b=?)) :}

$L e t f (x) = \sin^{3} (2 x) f o r - \frac{π}{4} ⩽ x ⩽ \frac{π}{4}$ $t h e n {D f}^{- 1} (\frac{1}{8}) = \frac{a}{b \sqrt{b}} s o {\begin{cases} a = ? \\ b = ? \end{cases}$

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