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AllQuestion and Answers: Page 1386

Question Number 67307 Answers: 1 Comments: 1

Question Number 67299 Answers: 2 Comments: 5

G(x)= (x+1)(x+3)Q(x) + px +q a) Given that G(x) leaves a remainder of 8 and −24 when divided by (x+1) and (x+3) respectively,find the remainder when G(x) is divided by (x+1)(x+3). b) Given that x+2 is a factor of G(x) and that the graph of G(x) passes through the point with coordinates (0,6) find G(x)

$G (x) = (x + 1) (x + 3) Q (x) + p x + q$ $a) G i v e n t h a t G (x) l e a v e s a r e m a i n d e r o f 8 a n d - 24 w h e n d i v i d e d b y (x + 1) a n d$ $(x + 3) r e s p e c t i v e l y, f i n d t h e r e m a i n d e r w h e n G (x) i s d i v i d e d b y (x + 1) (x + 3) .$ $b) G i v e n t h a t x + 2 i s a f a c t o r o f G (x) a n d t h a t t h e g r a p h o f G (x) p a s s e s t h r o u g h$ $t h e p o i n t w i t h c o o r d i n a t e s (0, 6) f i n d G (x)$

Question Number 67333 Answers: 0 Comments: 0

evaluate Σ_(n=0) ^(+∞) (1/((1+8n)^2 ))

$e v a l u a t e \underset{n = 0}{\sum^{+ \infty}} \frac{1}{{(1 + 8 n)}^{2}}$

Question Number 67281 Answers: 1 Comments: 6

Question Number 67337 Answers: 1 Comments: 0

m(p+1)=a ((q(p+1))/(r+1))=b & ((p(p+1))/(q+1))=c and ((r(p+1))/(m+1))=d find either of p,q,r,m in terms of a,b,c,d.

$m (p + 1) = a$ $\frac{q (p + 1)}{r + 1} = b & \frac{p (p + 1)}{q + 1} = c$ $a n d \frac{r (p + 1)}{m + 1} = d$ $f i n d e i t h e r o f p, q, r, m i n t e r m s o f$ $a, b, c, d .$

Question Number 67336 Answers: 0 Comments: 3

If (dy/dx) = e^(−t) (dy/dt) , find (d^2 y/dx^2 )

$If \frac{dy}{dx} = e^{- t} \frac{dy}{dt}, find \frac{d^{2} y}{{dx}^{2}}$

Question Number 67254 Answers: 1 Comments: 10

Question Number 67246 Answers: 2 Comments: 4

Integrate: 1) ∫_3 ^( ∞) ((1/x dx)/(ln(x)(√(ln^2 x−1)))) 2) ∫_1 ^∞ ((e^x dx)/(1+e^(2x) )) 3) ∫_1 ^∞ ((2^x dx)/(x+1)) 4) ∫_2 ^∞ ((√x)/(ln(x)))dx

$I n t e g r a t e :$ $1) \underset{3}{\int^{\infty}} \frac{1 / x d x}{l n (x) \sqrt{{l n}^{2} x - 1}}$ $2) \underset{1}{\int^{\infty}} \frac{e^{x} d x}{1 + e^{2 x}}$ $3) \underset{1}{\int^{\infty}} \frac{2^{x} d x}{x + 1}$ $4) \underset{2}{\int^{\infty}} \frac{\sqrt{x}}{l n (x)} d x$

Question Number 67244 Answers: 0 Comments: 7

Which of the series converge and which diverge? Check by the limit comparison test. 1) Σ_(n=2) ^∞ ((1+n ln(n))/(n^2 +5)) 2) Σ_(n=1) ^∞ ((ln(n))/n^(3/2) ) 3) Σ_(n=3) ^∞ (1/(ln(lnn))) 4) Σ_(n=1) ^∞ (1/(n (n)^(1/n) )) ??

$W h i c h o f t h e s e r i e s c o n v e r g e a n d$ $w h i c h d i v e r g e ? C h e c k b y t h e l i m i t$ $c o m p a r i s o n t e s t .$ $1) \underset{n = 2}{\sum^{\infty}} \frac{1 + n l n (n)}{n^{2} + 5}$ $2) \underset{n = 1}{\sum^{\infty}} \frac{l n (n)}{n^{\frac{3}{2}}}$ $3) \underset{n = 3}{\sum^{\infty}} \frac{1}{l n (l n n)}$ $4) \underset{n = 1}{\sum^{\infty}} \frac{1}{n {(n)}^{\frac{1}{n}}}$ $? ?$

Question Number 67236 Answers: 1 Comments: 1

let T_n =cos(narccosx) 1) calculste T_0 ,T_1 ,T_2 2)find roots of T_n 3)decompose the fraction F =(1/T_n )

$l e t T_{n} = c o s (n a r c c o s x)$ $1) c a l c u l s t e T_{0}, T_{1}, T_{2}$ $2) f i n d r o o t s o f T_{n}$ $3) d e c o m p o s e t h e f r a c t i o n F = \frac{1}{T_{n}}$

Question Number 67235 Answers: 0 Comments: 1

find ∫_(−(π/3)) ^(π/3) x^2 {cosx−sinx}^3 dx

$f i n d \int_{- \frac{π}{3}}^{\frac{π}{3}} x^{2} {c o s x - s i n x}^{3} d x$

Question Number 67234 Answers: 2 Comments: 3

factorise p(x)=1+x+x^2 +x^3 +x^5 inside C[x] and R[x] calculate p(e^(i(π/5)) ) and p(cos((π/5)))

$f a c t o r i s e p (x) = 1 + x + x^{2} + x^{3} + x^{5}$ $i n s i d e C [x] a n d R [x]$ $c a l c u l a t e p (e^{i \frac{π}{5}}) a n d p (c o s (\frac{π}{5}))$

Question Number 67233 Answers: 0 Comments: 1

calculate ∫_0 ^1 ((xdx)/(√(1+x^4 )))

$c a l c u l a t e \int_{0}^{1} \frac{x d x}{\sqrt{1 + x^{4}}}$

Question Number 67232 Answers: 1 Comments: 1

calculate Σ_(n=1) ^∞ ((cos(n(π/3)))/n)

$c a l c u l a t e \sum_{n = 1}^{\infty} \frac{c o s (n \frac{π}{3})}{n}$

Question Number 67231 Answers: 2 Comments: 0

find ∫x/x^5 −1) dx

$f i n d \int x / x^{5} - 1) d x$

Question Number 67298 Answers: 0 Comments: 2

Find the third degree polynomial which vanishes when x =−1 and x = 2, which has a value 8 when x =0 and leaves a remainder ((16)/3) when divided by 3x + 2.

$F i n d t h e t h i r d d e g r e e p o l y n o m i a l w h i c h v a n i s h e s w h e n$ $x = - 1 a n d x = 2, w h i c h h a s a v a l u e 8 w h e n x = 0 a n d l e a v e s a r e m a i n d e r \frac{16}{3} w h e n$ $d i v i d e d b y 3 x + 2 .$

Question Number 67294 Answers: 0 Comments: 3

solve for x and y the simultaneous equation log_3 x = y = log(2x − 1)

$s o l v e f o r x and y t h e s i m u l t a n e o u s e q u a t i o n$ $\log_{3} x = y = \log (2 x - 1)$

Question Number 67215 Answers: 1 Comments: 1

Question Number 67208 Answers: 1 Comments: 6

Find the times in a day when the hour′s, minute′s and second′s hand of a clock occupy the same angular position. [old question reposted]

$F i n d t h e t i m e s i n a d a y w h e n$ $t h e {h o u r}^{'} s, {m i n u t e}^{'} s a n d {s e c o n d}^{'} s$ $h a n d o f a c l o c k o c c u p y t h e s a m e$ $a n g u l a r p o s i t i o n .$ $[o l d q u e s t i o n r e p o s t e d]$

Question Number 67197 Answers: 1 Comments: 0

∫_0 ^2 x^5 (1−(x/2))^4 dx

$\int_{0}^{2} x^{5} {(1 - \frac{x}{2})}^{4} d x$

Question Number 67193 Answers: 0 Comments: 7

Question Number 67189 Answers: 1 Comments: 0

solve inside R^3 the system { ((2x+y+z =1)),((x+2y+z =2)) :} {x+y+2z =3

$s o l v e i n s i d e R^{3} t h e s y s t e m {\begin{cases} 2 x + y + z = 1 \\ x + 2 y + z = 2 \end{cases}$ ${x + y + 2 z = 3$

Question Number 67187 Answers: 0 Comments: 1

let f(x) =arctan(x^3 ) 1)calculate f^((n)) (x)and f^((n)) (0) 2) developp f at integr serie 3) calculate ∫_0 ^1 arctan(x^3 )dx

$l e t f (x) = a r c t a n (x^{3})$ $1) c a l c u l a t e f^{(n)} (x) a n d f^{(n)} (0)$ $2) d e v e l o p p f a t i n t e g r s e r i e$ $3) c a l c u l a t e \int_{0}^{1} a r c t a n (x^{3}) d x$

Question Number 67167 Answers: 4 Comments: 2

solve for real x and y:[a,b∈R] a. { ((x^3 +1=y^3 )),((x^2 +1=y^2 )) :} b. { ((x^3 +x^2 +1=y^3 )),((x^2 +x+1=y^2 )) :} c. { ((x^3 +y^2 =9xy)),((x^2 +y^3 =8xy)) :} d. { ((ax+by=2ab)),((x^2 +y^2 =4abxy)) :}

$solve for real x and y : [a, b \in R]$ $a . {\begin{cases} x^{3} + 1 = y^{3} \\ x^{2} + 1 = y^{2} \end{cases}$ $b . {\begin{cases} x^{3} + x^{2} + 1 = y^{3} \\ x^{2} + x + 1 = y^{2} \end{cases}$ $c . {\begin{cases} x^{3} + y^{2} = 9 xy \\ x^{2} + y^{3} = 8 xy \end{cases}$ $d . {\begin{cases} ax + by = 2 ab \\ x^{2} + y^{2} = 4 abxy \end{cases}$

Question Number 67153 Answers: 2 Comments: 0

find ∫(v^3 −2)/(v^4 +v )dv

$f i n d \int (v^{3} - 2) / (v^{4} + v) d v$

Question Number 67148 Answers: 0 Comments: 6

explicitez la suite u_n definie par la relation; { ((u_0 =0, u_1 =1)),((u_(n+2) =u_(n+1) +u_n ∀n∈∤N)) :} u_n =???????? −calculer la lim _(n→∞) (u_(n+1) /u_n )=??? −montre que Σ_(k=0) ^n u_k =u_(n+2) −1 voila^′

$explicitez la suite u_{n} definie par la relation;$ ${\begin{cases} u_{0} = 0, u_{1} = 1 \\ u_{n + 2} = u_{n + 1} + u_{n} \forall n \in∤ N \end{cases}$ $u_{n} = ? ? ? ? ? ? ? ?$ $- calculer la \lim \underset{n \to \infty}{} \frac{u_{n + 1}}{u_{n}} = ? ? ?$ $- montre que \underset{k = 0}{\sum^{n}} u_{k} = u_{n + 2} - 1$ ${voila}^{^{'}}$

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