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DifferentiationQuestion and Answers: Page 15

Question Number 159719 Answers: 1 Comments: 0

F(x)= 3cos x + 4sin x , F^((101)) ((π/2))=?

$F (x) = 3 \cos x + 4 \sin x, F^{(101)} (\frac{π}{2}) = ?$

Question Number 155857 Answers: 1 Comments: 0

1). Find (dy/dx) , if : a). y=(8x−1)(x^2 +4x+7) b). y=(3x^4 −10x+8)(2x^2 +5) 2). Find an equation of the tangen line to the graph of y=(5/(1+x^2 )) at each point a). P(0,5) b). Q(1,(5/2)) 3). Find the coordinat of all point on the graph of : y=x^3 +2x^2 −4x+5 at which the tangen line is: a). horizontal. b). paralel to the line y=2y+8x−5=0 4). Find point P on the graph of y=x^3 such that the tangen line at P has x−intercept 4 5). Find the points at which the graph f(x) and f^′ (x) is intersect , given that a). f(x)=x^3 −x^2 +x+1 b). f(x)=x^2 +2x+1

$1) . Find \frac{dy}{dx}, if :$ $a) . y = (8 x - 1) (x^{2} + 4 x + 7)$ $b) . y = ({3 x}^{4} - 10 x + 8) ({2 x}^{2} + 5)$ $2) . Find an equation of the tangen line$ $to the graph of y = \frac{5}{1 + x^{2}} at each point$ $a) . P (0, 5) b) . Q (1, \frac{5}{2})$ $3) . Find the coordinat of all point on$ $the graph of : y = x^{3} + {2 x}^{2} - 4 x + 5 at which the$ $tangen line is :$ $a) . horizontal .$ $b) . paralel to the line$ $y = 2 y + 8 x - 5 = 0$ $4) . Find point P on the graph of y = x^{3}$ $such that the tangen line at P has$ $x - intercept 4$ $5) . Find the points at which the graph$ $f (x) and f^{^{'}} (x) is intersect, given that$ $a) . f (x) = x^{3} - x^{2} + x + 1$ $b) . f (x) = x^{2} + 2 x + 1$

Question Number 155849 Answers: 0 Comments: 0

Ω=∫_0 ^( ∞) log(sinh(x)).log(tanh(x))dx=((7ζ(3))/8) +(π^( 2) /8)ln^ (2)

$Ω = \int_{0}^{\infty} l o g (s i n h (x)) . l o g (t a n h (x)) d x = \frac{7 ζ (3)}{8} + \frac{π^{2}}{8} {l n}^{} (2)$

Question Number 156776 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (n ln(((2n+1)/(2n−1))) −1)=?

$\underset{n = 1}{\sum^{\infty}} (n l n (\frac{2 n + 1}{2 n - 1}) - 1) = ?$

Question Number 155478 Answers: 1 Comments: 0

Π_(k = 1 ) ^n (1 + (1/k))^k = V_n find V_n

$\underset{k = 1}{\prod^{n}} {(1 + \frac{1}{k})}^{k} = V_{n}$ $f i n d V_{n}$

Question Number 155477 Answers: 1 Comments: 0

Question Number 155281 Answers: 1 Comments: 0

f :[ 0 , 6] → [−4 , 4] f (0 )=0 f (6 )=4 x, y≥0 , x+y ≤6 f (x+y )=(1/4){f(x)(√(16−(f(y))^2 )) +f(y)(√(16−(f(x))^2 )) } ∴ ( f(1) +f (3))^( 2) =?

$f : [0, 6] \to [- 4, 4]$ $f (0) = 0$ $f (6) = 4$ $x, y ⩾ 0, x + y ⩽ 6$ $f (x + y) = \frac{1}{4} {f (x) \sqrt{16 - {(f (y))}^{2}} + f (y) \sqrt{16 - {(f (x))}^{2}}}$ $∴ {(f (1) + f (3))}^{2} = ?$

Question Number 155237 Answers: 1 Comments: 0

If Ω = ∫_0 ^( ∞) (( ln^( 2) (x ).sin((√(x )) ))/x) dx prove that : Ω = 4 γ^( 2) + (π^( 3) /3) ■ m.n

$I f Ω = \int_{0}^{\infty} \frac{{l n}^{2} (x) . s i n (\sqrt{x})}{x} d x$ $p r o v e t h a t :$ $Ω = 4 γ^{2} + \frac{π^{3}}{3} ◼ m . n$

Question Number 155203 Answers: 1 Comments: 0

Question Number 154940 Answers: 1 Comments: 0

Question Number 154478 Answers: 1 Comments: 0

prove that # ∫_0 ^( ∞) (( sin^( 3) ( x ).ln( x ))/x) dx =^? (π/8) (−2γ +ln(3)) .....■ m.n

$You can't use 'macro parameter character #' in math mode$ $\int_{0}^{\infty} \frac{{s i n}^{3} (x) . l n (x)}{x} d x \overset{?}{=} \frac{π}{8} (- 2 γ + l n (3)) . . . . . ◼ m . n$

Question Number 154250 Answers: 0 Comments: 0

Question Number 154058 Answers: 1 Comments: 0

Question Number 153956 Answers: 2 Comments: 0

Max & min value of function f(x)=(√(6−x)) +(√(12+x)) .

$M a x & m i n v a l u e o f f u n c t i o n$ $f (x) = \sqrt{6 - x} + \sqrt{12 + x} .$

Question Number 153934 Answers: 0 Comments: 0

Question Number 153862 Answers: 0 Comments: 0

Question Number 153553 Answers: 1 Comments: 0

sin(9) + sin(21)+sin(39)=^? (ϕ/( (√2))) ϕ:= golden ratio m.n

$s i n (9) + s i n (21) + s i n (39) \overset{?}{=} \frac{φ}{\sqrt{2}}$ $φ := g o l d e n r a t i o$ $m . n$

Question Number 153340 Answers: 1 Comments: 0

Solve .. x , y , z ∈ R^( +) & x+ y= z K := Min_ ((( x^( 4) + y^( 4) + z^( 4) )/(x^( 2) y^( 2) )) ) = ? ■ Source : Elementary Olympid Book m.n

$Solve . .$ $x, y, z \in R^{+} & x + y = z$ $K := {Min}_{} (\frac{x^{4} + y^{4} + z^{4}}{x^{2} y^{2}}) = ? ◼$ $Source : Elementary Olympid Book m . n$

Question Number 153252 Answers: 1 Comments: 0

Question Number 153212 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) (( tan(x).Arctanh(cos(x)))/x)dx=?

$\int_{- \infty}^{\infty} \frac{t a n (x) . A r c t a n h (c o s (x))}{x} d x = ?$

Question Number 153189 Answers: 2 Comments: 0

Question Number 152947 Answers: 1 Comments: 0

prove :: 𝛗=∫_(−∞) ^( ∞) (( e^( −(1/x^( 2) )) )/x^( 4) ) dx =^? (1/2) Γ ((1/2) )

$p r o v e ::$ $ϕ = \int_{- \infty}^{\infty} \frac{e^{- \frac{1}{x^{2}}}}{x^{4}} d x \overset{?}{=} \frac{1}{2} Γ (\frac{1}{2})$

Question Number 152904 Answers: 5 Comments: 0

Question Number 152795 Answers: 1 Comments: 0

𝛗=∫_0 ^( ∞) ((sin(x ))/x)(((a^( 2) +cos^( 2) (x))/(b^( 2) + cos^( 2) (x ))))dx=?

$ϕ = \int_{0}^{\infty} \frac{s i n (x)}{x} (\frac{a^{2} + {c o s}^{2} (x)}{b^{2} + {c o s}^{2} (x)}) d x = ?$

Question Number 152761 Answers: 0 Comments: 0

prove that: S := Σ_(n=1) ^∞ ((( 1)/(sinh (2^( n) .x)))) =^? (( 2)/(e^( 2x) −1)) m.n...

$p r o v e t h a t :$ $S := \underset{n = 1}{\sum^{\infty}} (\frac{1}{s i n h (2^{n} . x)}) \overset{?}{=} \frac{2}{e^{2 x} - 1}$ $m . n . . .$

Question Number 152797 Answers: 1 Comments: 0

nice..mathematics... Prove that... I= ∫_0 ^( ∞) (( cos (x ))/(cosh (x ))) dx=(π/( cosh ((π/2) ))) .......■ prepared :: m.n

$n i c e . . m a t h e m a t i c s . . .$ $Prove that . . .$ $I = \int_{0}^{\infty} \frac{c o s (x)}{c o s h (x)} d x = \frac{π}{c o s h (\frac{π}{2})} . . . . . . . ◼$ $p r e p a r e d :: m . n$

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