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AllQuestion and Answers: Page 1472

Question Number 57416 Answers: 0 Comments: 1

let f(x)=∫_(2x) ^(4x) (dt/(t^2 −2t +3)) 1)find f(x) 2) calculate lim_(x→0) f(x) and lim_(x→+∞) f(x)

$l e t f (x) = \int_{2 x}^{4 x} \frac{d t}{t^{2} - 2 t + 3}$ $1) f i n d f (x)$ $2) c a l c u l a t e {l i m}_{x \to 0} f (x) a n d {l i m}_{x \to + \infty} f (x)$

Question Number 57415 Answers: 0 Comments: 1

solve (x−1)y^′ +(1+(√x))y =x e^(−2x)

$s o l v e (x - 1) y^{^{'}} + (1 + \sqrt{x}) y = x e^{- 2 x}$

Question Number 57414 Answers: 0 Comments: 2

solve y′ =2y^2 +y and y(o)=1

$s o l v e y^{'} = 2 y^{2} + y a n d y (o) = 1$

Question Number 57413 Answers: 0 Comments: 0

prove that ln(1+x)>((arctanx)/(1+x)) ∀x>0

$p r o v e t h a t l n (1 + x) > \frac{a r c t a n x}{1 + x} \forall x > 0$

Question Number 57412 Answers: 0 Comments: 1

let u_n =1 +(1/(√2)) +(1/(√3)) +...+(1/(√n)) prove that (u_n ) is divdrgente.

$l e t u_{n} = 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + . . . + \frac{1}{\sqrt{n}}$ $p r o v e t h a t (u_{n}) i s d i v d r g e n t e .$

Question Number 57411 Answers: 1 Comments: 1

let f(x)=arctan((√x)+(√(x+1))) find f^(−1) (x) .

$l e t f (x) = a r c t a n (\sqrt{x} + \sqrt{x + 1})$ $f i n d f^{- 1} (x) .$

Question Number 57410 Answers: 1 Comments: 1

find lim_(x→1) ((sin(x^5 +x−2))/(x−1))

$f i n d {l i m}_{x \to 1} \frac{s i n (x^{5} + x - 2)}{x - 1}$

Question Number 57409 Answers: 0 Comments: 1

let S_n =Σ_(k=1) ^(2n+1) (1/(√(n^2 +k))) calculste lim_(n→+∞) S_n

$l e t S_{n} = \sum_{k = 1}^{2 n + 1} \frac{1}{\sqrt{n^{2} + k}}$ $c a l c u l s t e {l i m}_{n \to + \infty} S_{n}$

Question Number 57408 Answers: 0 Comments: 0

let the sequence (a_n ) wich verify a_1 =2 and a_(n+1) =a_n +(√(1+(a_n /n))) prove that ((a_n /n))_(n≥1) is convergente.

$l e t t h e s e q u e n c e (a_{n}) w i c h v e r i f y a_{1} = 2 a n d$ $a_{n + 1} = a_{n} + \sqrt{1 + \frac{a_{n}}{n}}$ $p r o v e t h a t {(\frac{a_{n}}{n})}_{n ⩾ 1} i s c o n v e r g e n t e .$

Question Number 57407 Answers: 0 Comments: 1

let U_0 =cos((π/3)) and U_(n+1) =(√((1+U_n )/2)) find U_n interms of n .

$l e t U_{0} = c o s (\frac{π}{3}) a n d U_{n + 1} = \sqrt{\frac{1 + U_{n}}{2}}$ $f i n d U_{n} i n t e r m s o f n .$

Question Number 57406 Answers: 0 Comments: 1

let f(x)=(x/(√(1+x^2 ))) +cos(πx) 1) prove that f(x)=0 have a solurion α inside ]0,1[ 2) use newton method to find a approximate value of α .

$l e t f (x) = \frac{x}{\sqrt{1 + x^{2}}} + c o s (π x)$ $1) p r o v e t h a t f (x) = 0 h a v e a s o l u r i o n α i n s i d e] 0, 1 [$ $2) u s e n e w t o n m e t h o d t o f i n d a a p p r o x i m a t e$ $v a l u e o f α .$

Question Number 57405 Answers: 1 Comments: 0

calculate lim_(x→0) ((1−cosx.cos(2x)....cos(nx))/x^2 ) with n integr natural not 0.

$c a l c u l a t e {l i m}_{x \to 0} \frac{1 - c o s x . c o s (2 x) . . . . c o s (n x)}{x^{2}}$ $w i t h n i n t e g r n a t u r a l n o t 0 .$

Question Number 57404 Answers: 1 Comments: 5

find lim_(x→0) ((sin(π(√(cosx))))/x^2 )

$f i n d {l i m}_{x \to 0} \frac{s i n (π \sqrt{c o s x})}{x^{2}}$

Question Number 57400 Answers: 0 Comments: 1

Question Number 57390 Answers: 0 Comments: 0

a^2 + d^2 − ad = b^2 + c^2 + bc a^2 + b^2 = c^2 + d^2 ((ab + cd)/(ad + bc)) = ?

$a^{2} + d^{2} - a d = b^{2} + c^{2} + b c$ $a^{2} + b^{2} = c^{2} + d^{2}$ $\frac{a b + c d}{a d + b c} = ?$

Question Number 57389 Answers: 1 Comments: 0

If aεR and the equation : −3{x}^2 +2{x}+a^2 =0 has no integral solution, then all possible value of a lie in the interval : (a)(−1,0)U(0,1) (b)(1,2) (c) (−2,−1) (d)(−∞,−2)U(2,∞)

$I f a ϵ R a n d t h e e q u a t i o n :$ $- 3 {x}^{2} + 2 {x} + a^{2} = 0 h a s n o i n t e g r a l$ $s o l u t i o n, t h e n a l l p o s s i b l e v a l u e o f a$ $l i e i n t h e i n t e r v a l :$ $(a) (- 1, 0) U (0, 1) (b) (1, 2)$ $(c) (- 2, - 1) (d) (- \infty, - 2) U (2, \infty)$

Question Number 57388 Answers: 0 Comments: 0

Given f(x) = f(x + 2016), ∀x ∈ R If ∫_0 ^3 f(x) = 30, then ∫_3 ^5 f(x + 2016) = ...

$Given f (x) = f (x + 2016), \forall x \in R$ $If \underset{0}{\int^{3}} f (x) = 30, then \underset{3}{\int^{5}} f (x + 2016) = . . .$

Question Number 57387 Answers: 0 Comments: 0

Question Number 57385 Answers: 1 Comments: 1

Question Number 57383 Answers: 1 Comments: 1

Question Number 57381 Answers: 0 Comments: 0

Question Number 57377 Answers: 0 Comments: 0

Can i find the sum of a product to infinity ? e.g 1.2.3.4.5 .... infinity

$Can i find the sum of a product to infinity ?$ $e . g 1.2.3.4.5 . . . . infinity$

Question Number 57373 Answers: 1 Comments: 1

tan 1°+tan 5°+tan 9°+…+tan 177°=...

$\tan 1 ° + \tan 5 ° + \tan 9 ° + \dots + \tan 177 ° = . . .$

Question Number 57368 Answers: 1 Comments: 0

5^(3x−3) −5^(3x) −5=615 solve for x

$5^{3 x - 3} - 5^{3 x} - 5 = 615$ $solve for x$

Question Number 57363 Answers: 0 Comments: 3

Question Number 57357 Answers: 3 Comments: 2

1−2sin(4x)<cos^2 (4x) solve.

$1 - 2 \sin (4 x) < \cos^{2} (4 x)$ $solve .$

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