Question and Answers Forum

let g(x)=(√(−x+(√(1+x^2 )))) 1) prove that g is solution for the differencial equation 4(1+x^2 )y^(′′) +4xy^′ −y =0 .prove that g is C^∞ on R 2) determine a relation between g^((n)) (0) and g^((n+2)) (0)

$l e t g (x) = \sqrt{- x + \sqrt{1 + x^{2}}}$ $1) p r o v e t h a t g i s s o l u t i o n f o r t h e d i f f e r e n c i a l e q u a t i o n$ $4 (1 + x^{2}) y^{^{″}} + 4 {x y}^{^{'}} - y = 0 . p r o v e t h a t g i s C^{\infty} o n R$ $2) d e t e r m i n e a r e l a t i o n b e t w e e n g^{(n)} (0) a n d g^{(n + 2)} (0)$

Question Number 40102 Answers: 2 Comments: 0

let f(x) = ((∣x∣)/((1+∣1−x^2 ∣)^n )) study tbe derivability of f at points 0 and 1 (n natural integr)

$l e t f (x) = \frac{∣ x ∣}{{(1 + ∣ 1 - x^{2} ∣)}^{n}}$ $s t u d y t b e d e r i v a b i l i t y o f f a t p o i n t s 0 a n d 1 (n n a t u r a l i n t e g r)$

Question Number 40101 Answers: 0 Comments: 0

study the variation of f(x)=arcsin(2x(√(1−x^2 )) ) and give its graph

$s t u d y t h e v a r i a t i o n o f f (x) = a r c s i n (2 x \sqrt{1 - x^{2}}) a n d g i v e i t s g r a p h$

Question Number 40100 Answers: 0 Comments: 1

solve arctan(2x) +arctan(3x)=(π/4)

$s o l v e a r c t a n (2 x) + a r c t a n (3 x) = \frac{π}{4}$

Question Number 40099 Answers: 0 Comments: 0

solve arcsin(((2x)/(1+x^2 ))) =(π/3)

$s o l v e a r c s i n (\frac{2 x}{1 + x^{2}}) = \frac{π}{3}$

Question Number 40098 Answers: 0 Comments: 0

solve arcsin(sinx) =(π/9)

$s o l v e a r c s i n (s i n x) = \frac{π}{9}$

Question Number 40097 Answers: 0 Comments: 2

let f(x)=ln(√((2+x)/(2−x))) 1) find D_f and find the assymptotes to C_f 2) calculate f^′ (x) and give the variation of f 3) give the graph of f 4) give the equation of tangent to C_(f ) at point E((1/2),f((1/2))) 5) calculate ∫_0 ^1 f(x)dx .

$l e t f (x) = l n \sqrt{\frac{2 + x}{2 - x}}$ $1) f i n d D_{f} a n d f i n d t h e a s s y m p t o t e s t o C_{f}$ $2) c a l c u l a t e f^{^{'}} (x) a n d g i v e t h e v a r i a t i o n o f f$ $3) g i v e t h e g r a p h o f f$ $4) g i v e t h e e q u a t i o n o f t a n g e n t t o C_{f} a t p o i n t E (\frac{1}{2}, f (\frac{1}{2}))$ $5) c a l c u l a t e \int_{0}^{1} f (x) d x .$

Question Number 40095 Answers: 1 Comments: 0

let f(x) =cos(x)cos((1/x)) is f have a limit at point 0?

$l e t f (x) = c o s (x) c o s (\frac{1}{x}) i s f h a v e a l i m i t a t p o i n t 0 ?$

Question Number 40094 Answers: 0 Comments: 0

find lim _(x→0^+ ) ln(x)tan{ln(1+x)}

$f i n d l i m_{x \to 0^{+}} l n (x) t a n {l n (1 + x)}$

Question Number 40093 Answers: 0 Comments: 0

find lim _(x→0) ((ln(cosx))/(1−cos(2x)))

$f i n d l i m_{x \to 0} \frac{l n (c o s x)}{1 - c o s (2 x)}$

Question Number 40092 Answers: 0 Comments: 1

calculate lim_(x→+∞) (1/x) tan(((πx)/(2x+3)))

$c a l c u l a t e {l i m}_{x \to + \infty} \frac{1}{x} t a n (\frac{π x}{2 x + 3})$

Pg 1622 Pg 1623 Pg 1624 Pg 1625 Pg 1626 Pg 1627 Pg 1628 Pg 1629 Pg 1630 Pg 1631

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