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Question Number 37961 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) .

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{x^{2} + \sqrt{1 + x^{2}}} .$

Question Number 37957 Answers: 0 Comments: 0

Question Number 37953 Answers: 0 Comments: 1

Question Number 37948 Answers: 0 Comments: 1

If x ∈R show that (2+i)e^((1+3i)) +(2−i)e^((1−3i)) is also real.

$I f x \in R$ $s h o w t h a t (2 + i) e^{(1 + 3 i)} + (2 - i) e^{(1 - 3 i)} i s a l s o r e a l .$

Question Number 37940 Answers: 1 Comments: 0

Which of the following expressions are positive for all real values of x? a) x^2 − 2x + 5 b) x^2 −2x−1 c) x^2 +4x+2 d) 2x^2 −6x + 5

$W h i c h o f t h e f o l l o w i n g$ $e x p r e s s i o n s a r e p o s i t i v e f o r$ $a l l r e a l v a l u e s o f x ?$ $a) x^{2} - 2 x + 5 b) x^{2} - 2 x - 1$ $c) x^{2} + 4 x + 2 d) 2 x^{2} - 6 x + 5$

Question Number 37938 Answers: 5 Comments: 5

Question Number 37945 Answers: 0 Comments: 10

Two plane mirrors are inclined at an angle of 30°.A ray of light which makes an angle of incidence of 50° with one of the mirrors,undergoes two successive reflections at the mirrors.Calculate the angle of deviation. please help....its urgent

$T w o p l a n e m i r r o r s a r e i n c l i n e d a t$ $a n a n g l e o f 30 ° . A r a y o f l i g h t w h i c h$ $m a k e s a n a n g l e o f i n c i d e n c e o f 50 °$ $w i t h o n e o f t h e m i r r o r s, u n d e r g o e s$ $t w o s u c c e s s i v e r e f l e c t i o n s a t t h e$ $m i r r o r s . C a l c u l a t e t h e a n g l e o f$ $d e v i a t i o n .$ $p l e a s e h e l p . . . . i t s u r g e n t$

Question Number 37930 Answers: 1 Comments: 1

n∈N U_(n+1) =((1/2))^(n+1) +U_n U_n =?

$n \in N$ $U_{n + 1} = {(\frac{1}{2})}^{n + 1} + U_{n}$ $U_{n} = ?$

Question Number 37922 Answers: 1 Comments: 2

f : N → R g : N → R f(n)=∫_0 ^(2π) x^n sin x dx g(n)=∫_0 ^(2π) x^n cos x dx ((f(n+1)−f(n))/(g(n+1)−g(n)))=?

$f : N \to R$ $g : N \to R$ $f (n) = \int_{0}^{2 π} x^{n} \sin x d x$ $g (n) = \int_{0}^{2 π} x^{n} \cos x d x$ $\frac{f (n + 1) - f (n)}{g (n + 1) - g (n)} = ?$

Question Number 37915 Answers: 1 Comments: 0

If y=4x^2 −1 , then find ((85)/(169))+Σ_(i=1) ^(84) (1/(y(i)))

$If y = 4 x^{2} - 1, then find$ $\frac{85}{169} + \underset{i = 1}{\overset{84}{Σ}} \frac{1}{y (i)}$

Question Number 37914 Answers: 1 Comments: 0

In △ABC, if sin A=sin^2 B then prove 4 cos 2A−4 cos 2B=1−cos 4B

$In △ A B C, if \sin A = \sin^{2} B$ $then prove$ $4 \cos 2 A - 4 \cos 2 B = 1 - \cos 4 B$

Question Number 37913 Answers: 1 Comments: 0

Solve the diferential equatuion (dy/dx)=((2x+y+1)/(x−2y+3))

$Solve the diferential equatuion$ $\frac{d y}{d x} = \frac{2 x + y + 1}{x - 2 y + 3}$

Question Number 37912 Answers: 1 Comments: 1

Evaluate : the Integral ∫_(-(π/2)) ^(π/2) ∫_0 ^(3 cos θ) r^2 sin^2 θ. dr dθ

$Evaluate : the Integral$ $\int_{- \frac{π}{2}}^{\frac{π}{2}} \int_{0}^{3 \cos θ} r^{2} \sin^{2} θ . d r d θ$

Question Number 37911 Answers: 0 Comments: 1

the function f(x) is defined by f(x) = { ((−x + 1 , for x≤3)),((kx − 8 , for x ≥ 3)) :} find the value of k .

$the function f (x) is defined by$ $f (x) = {\begin{cases} - x + 1, f o r x ⩽ 3 \\ k x - 8, f o r x ⩾ 3 \end{cases}$ $f i n d t h e v a l u e o f k .$

Question Number 37906 Answers: 1 Comments: 0

Question Number 37902 Answers: 2 Comments: 1

ind the value of f(a) =∫_0 ^(+∞) (dx/(x^2 +(√(a^2 +x^2 )))) dx witha>0 2)calculate f^′ (a) .

$i n d t h e v a l u e o f f (a) = \int_{0}^{+ \infty} \frac{d x}{x^{2} + \sqrt{a^{2} + x^{2}}} d x$ $w i t h a > 0$ $2) c a l c u l a t e f^{^{'}} (a) .$

Question Number 37901 Answers: 0 Comments: 1

let f(x)= (1+e^(−x) )^n 1) calculate f^((p)) (x) and f^((p)) (o) 2)calculate f^((n)) (0) 3)developp f at integr serie .

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

Question Number 37898 Answers: 1 Comments: 1

calculate f(λ) = ∫_0 ^(+∞) e^(−λx) cos(π[x])dx withλ>0

$c a l c u l a t e f (λ) = \int_{0}^{+ \infty} e^{- λ x} c o s (π [x]) d x$ $w i t h λ > 0$

Question Number 37896 Answers: 2 Comments: 1

let I_n = ∫_0 ^n (((−1)^([x]) )/((2x+1)^2 ))dx 1) calculate I_n interms of n 2) find lim_(n→+∞) I_n

$l e t I_{n} = \int_{0}^{n} \frac{{(- 1)}^{[x]}}{{(2 x + 1)}^{2}} d x$ $1) c a l c u l a t e I_{n} i n t e r m s o f n$ $2) f i n d {l i m}_{n \to + \infty} I_{n}$

Question Number 37895 Answers: 1 Comments: 0

calculate A_n =∫_0 ^n (x−[(√x)])dx and lim_(n→+∞) A_n

$c a l c u l a t e A_{n} = \int_{0}^{n} (x - [\sqrt{x}]) d x a n d$ ${l i m}_{n \to + \infty} A_{n}$

Question Number 37894 Answers: 0 Comments: 0

find nature of the serie Σ_(n=1) ^∞ (Σ_(k=0) ^n (1/C_n ^k ))x^n

$f i n d n a t u r e o f t h e s e r i e$ $\sum_{n = 1}^{\infty} (\sum_{k = 0}^{n} \frac{1}{C_{n}^{k}}) x^{n}$

Question Number 37893 Answers: 1 Comments: 1

calculate ∫_0 ^1 (√(x+(√(x+1)))) dx .

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

Question Number 37892 Answers: 0 Comments: 3

let f(x)=(√(x+(√(x+1)))) 1) find D_f 2) give the equation of assymtote at point A(0,f(o)) 3) if f(x)∼ a(x−1) +b (x→1) determine a andb 4) calculate f^′ (x) 5) find f^(−1) (x) and (f^(−1) )^′ (x)

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

Question Number 37891 Answers: 0 Comments: 1

calculate B_n = Σ_(k=0) ^n (−1)^k (2k^2 +1) interms of n.

$c a l c u l a t e B_{n} = \sum_{k = 0}^{n} {(- 1)}^{k} (2 k^{2} + 1) i n t e r m s o f n .$

Question Number 37890 Answers: 0 Comments: 2

calculate A_n = Σ_(k=0) ^n (−1)^k (2k+3) interms of n

$c a l c u l a t e A_{n} = \sum_{k = 0}^{n} {(- 1)}^{k} (2 k + 3) i n t e r m s o f n$

Question Number 37889 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x))/x) e^(−tx) dx with t ≥0

$c a l c u l a t e \int_{0}^{\infty} \frac{a r c t a n (2 x)}{x} e^{- t x} d x w i t h t ⩾ 0$

Pg 1632 Pg 1633 Pg 1634 Pg 1635 Pg 1636 Pg 1637 Pg 1638 Pg 1639 Pg 1640 Pg 1641

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