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DifferentiationQuestion and Answers: Page 10

Question Number 166435 Answers: 2 Comments: 0

Equation : Solve in R ⌊x⌋ +⌊2x ⌋ +⌊ 3x ⌋=1 −−−−−−−−−

$E q u a t i o n :$ $S o l v e i n R$ $⌊ x ⌋ + ⌊ 2 x ⌋ + ⌊ 3 x ⌋ = 1$ $- - - - - - - - -$

Question Number 166331 Answers: 2 Comments: 1

prove that ((df^(−1) (a))/dx)×((df(f^(−1) (a)))/dx)=1

$p r o v e t h a t$ $\frac{{d f}^{- 1} (a)}{d x} \times \frac{d f (f^{- 1} (a))}{d x} = 1$

Question Number 166294 Answers: 0 Comments: 5

f(x)=∫_1 ^x (dt/( (√(t^3 +2t^2 +3)))) (f^(−1) (0))′=?

$f (x) = \int_{1}^{x} \frac{d t}{\sqrt{t^{3} + 2 t^{2} + 3}}$ ${(f^{- 1} (0))}^{'} = ?$

Question Number 166254 Answers: 1 Comments: 0

Θ=Σ_(n=1) ^∞ (( H_( n) )/(n. (n+1 ))) =^? (π^( 2) /6) −−−−+

$Θ = \underset{n = 1}{\sum^{\infty}} \frac{H_{n}}{n . (n + 1)} \overset{?}{=} \frac{π^{2}}{6}$ $- - - - +$

Question Number 166257 Answers: 1 Comments: 2

⌊x⌋⌊2x⌋⌊3x⌋= 6 x=?^

$⌊ x ⌋ ⌊ 2 x ⌋ ⌊ 3 x ⌋ = 6$ $x = \overset{}{?}$

Question Number 166246 Answers: 1 Comments: 0

Question Number 166082 Answers: 1 Comments: 0

prove Ω = ∫_0 ^( 1) (( (1−x )^( 2) .ln^( 3) (1−x ))/x) dx = ((51)/8) −(π^( 4) /(15)) ■ m.n

$p r o v e$ $Ω = \int_{0}^{1} \frac{{(1 - x)}^{2} . {l n}^{3} (1 - x)}{x} d x = \frac{51}{8} - \frac{π^{4}}{15} ◼ m . n$

Question Number 165849 Answers: 0 Comments: 1

solve the differential equation (dy/dx)+(y/(x−1))=(1/(x+1))

$s o l v e t h e d i f f e r e n t i a l e q u a t i o n$ $\frac{d y}{d x} + \frac{y}{x - 1} = \frac{1}{x + 1}$

Question Number 165746 Answers: 1 Comments: 0

compute the extreme points of: f=e^x sin(x+y)

$c o m p u t e t h e e x t r e m e p o i n t s o f :$ $f = e^{x} s i n (x + y)$

Question Number 165687 Answers: 2 Comments: 0

If f(x)= ((x^( 2) − 2x −8)/(x^( 2) −7x +12)) then ,find : f^( −1) (x)=?

$I f f (x) = \frac{x^{2} - 2 x - 8}{x^{2} - 7 x + 12}$ $t h e n, f i n d : f^{- 1} (x) = ?$

Question Number 165641 Answers: 2 Comments: 0

Given that y = (1/x) (a) Show that y^((n)) = (((−1)^n n!)/x^(n+1) ) (b) Find an expression for y^((n−1)) + y^((n))

$Given that y = \frac{1}{x}$ $(a) Show that y^{(n)} = \frac{{(- 1)}^{n} n!}{x^{n + 1}}$ $(b) Find an expression for y^{(n - 1)} + y^{(n)}$

Question Number 165599 Answers: 1 Comments: 0

Question Number 165597 Answers: 0 Comments: 0

prove that Σ_(n=1) ^∞ (( ψ^( (1)) (n))/n^( 2) ) =(7/4) ζ (4) ■ m.n

$p r o v e t h a t$ $\underset{n = 1}{\sum^{\infty}} \frac{ψ^{(1)} (n)}{n^{2}} = \frac{7}{4} ζ (4) ◼ m . n$

Question Number 165581 Answers: 2 Comments: 0

ϕ(t)=∫_0 ^( (π/2)) ( sin(x)+t cos(x))^( 2) dx find the value of the extermum of ϕ (t).

$φ (t) = \int_{0}^{\frac{π}{2}} {(s i n (x) + t c o s (x))}^{2} d x$ $f i n d t h e v a l u e o f t h e e x t e r m u m$ $o f φ (t) .$

Question Number 165471 Answers: 0 Comments: 1

{ ((h(3x)=(((2−x)/(x+1))−f(x^3 ))^2 )),((f(1)=f ′(1)=2)) :} h ′(3)=?

${\begin{cases} h (3 x) = {(\frac{2 - x}{x + 1} - f (x^{3}))}^{2} \\ f (1) = f^{'} (1) = 2 \end{cases}$ $h^{'} (3) = ?$

Question Number 165441 Answers: 1 Comments: 0

Question Number 165328 Answers: 3 Comments: 0

prove that Nice Integral 𝛗=∫_0 ^( 1) (( tan^( −1) (x^( (3/2)) ))/x^( 2) ) dx =((π + (√3) ln(7 +4(√3) ))/4) ■ m.n −−−−−−−−−

$p r o v e t h a t$ $N i c e I n t e g r a l$ $ϕ = \int_{0}^{1} \frac{{t a n}^{- 1} (x^{\frac{3}{2}})}{x^{2}} d x = \frac{π + \sqrt{3} l n (7 + 4 \sqrt{3})}{4} ◼ m . n$ $- - - - - - - - -$

Question Number 165194 Answers: 2 Comments: 0

∫_0 ^( 2π) ln ( 1+ cos (x)).cos (nx )dx=?

$\int_{0}^{2 π} l n (1 + c o s (x)) . c o s (n x) d x = ?$

Question Number 165168 Answers: 1 Comments: 0

Question Number 165152 Answers: 1 Comments: 0

prove Ω=∫_0 ^( 1) (( x − x^( 2) )/((1+x )ln(x))) dx = ln((4/π) ) −−−−−

$p r o v e$ $Ω = \int_{0}^{1} \frac{x - x^{2}}{(1 + x) l n (x)} d x = l n (\frac{4}{π})$ $- - - - -$

Question Number 165018 Answers: 0 Comments: 0

y = Γ(m+n) Find (dy/dn)

$y = Γ (m + n)$ $F i n d \frac{d y}{d n}$

Question Number 164747 Answers: 1 Comments: 0

faind (dy/dx) sin^(−1) (xy)=csc^(−1) (x−y)

$f a i n d \frac{d y}{d x}$ ${s i n}^{- 1} (x y) = {c s c}^{- 1} (x - y)$

Question Number 164716 Answers: 1 Comments: 0

find minimum value of f(x)=4sin 2x−5sin x−5cos x+6

$f i n d m i n i m u m v a l u e o f$ $f (x) = 4 \sin 2 x - 5 \sin x - 5 \cos x + 6$

Question Number 164671 Answers: 1 Comments: 1

solve cos^( 3) (x) + sin^( 2) (x) = (7/8) adopted from youtube ...

$s o l v e$ ${c o s}^{3} (x) + {s i n}^{2} (x) = \frac{7}{8}$ $a d o p t e d f r o m y o u t u b e . . .$

Question Number 164653 Answers: 2 Comments: 0

solve 𝛗 = ∫_0 ^( 1) ((ln^( 2) ( x ). tanh^( −1) ( x ))/x)dx =? Ω= ∫_0 ^( 1) (( (tanh^(−1) (x))^( 2) )/(1+x)) = ? −−−−

$s o l v e$ $ϕ = \int_{0}^{1} \frac{\ln^{2} (x) . {t a n h}^{- 1} (x)}{x} d x = ?$ $Ω = \int_{0}^{1} \frac{{({t a n h}^{- 1} (x))}^{2}}{1 + x} = ?$ $- - - -$

Question Number 164547 Answers: 1 Comments: 0

prove Ω= ∫_0 ^( ∞) (( (√x))/(( 1+x +x^( 2) )^( 3) )) dx =^? ((π(√3))/(36)) −−m.n−−

$p r o v e$ $Ω = \int_{0}^{\infty} \frac{\sqrt{x}}{{(1 + x + x^{2})}^{3}} d x \overset{?}{=} \frac{π \sqrt{3}}{36}$ $- - m . n - -$

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