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Question Number 31946 Answers: 0 Comments: 0

Calculate Σ_(j≤k≤i) (−1)^k ((i),(k) ) ((k),(j) )

$Calculate \underset{j ⩽ k ⩽ i}{Σ} {(- 1)}^{k} (\begin{matrix} i \\ k \end{matrix}) (\begin{matrix} k \\ j \end{matrix})$

Question Number 31743 Answers: 1 Comments: 0

Find the value of : Σ_(i=0) ^∞ Σ_(j=0) ^∞ Σ_(k=0) ^∞ (1/(3^i 3^j 3^k )). case 1: i≠j≠k. case 2: i<j<k.

$F i n d t h e v a l u e o f : \underset{i = 0}{\sum^{\infty}} \underset{j = 0}{\sum^{\infty}} \underset{k = 0}{\sum^{\infty}} \frac{1}{3^{i} 3^{j} 3^{k}} .$ $c a s e 1 : i \neq j \neq k .$ $c a s e 2 : i < j < k .$

Question Number 31674 Answers: 0 Comments: 0

let p_n (x) polinom Maclaurin for function f(x)=e^x . How many degree minimal polinom (n) so ∣e^x −p_n (x)∣≤ 10^(−2) , for −1≤x≤1?

$let p_{n} (x) polinom Maclaurin for$ $function f (x) = e^{x} . How many$ $degree minimal polinom (n) so$ $∣ e^{x} - p_{n} (x) ∣⩽ 10^{- 2}, for - 1 ⩽ x ⩽ 1 ?$

Question Number 31671 Answers: 0 Comments: 0

let f diferensiabel on continues x=a and f(a)≠ 0 lim_(n→∞) [((f(a+(1/n)))/(f(a)))]^n value is ?

$let f diferensiabel on continues$ $x = a and f (a) \neq 0$ $\lim_{n \to \infty} {[\frac{f (a + \frac{1}{n})}{f (a)}]}^{n}$ $value is ?$

Question Number 31583 Answers: 0 Comments: 0

how to read this ⟨x⟩. p

$h o w t o r e a d t h i s ⟨ x ⟩ . p$

Question Number 31569 Answers: 1 Comments: 0

(a,(1/a)),(b,(1/b)),(c,(1/c)),(d,(1/d)) are four distinct points on a circle of radius is 4 units then abcd is equal to ?

$(a, \frac{1}{a}), (b, \frac{1}{b}), (c, \frac{1}{c}), (d, \frac{1}{d}) a r e f o u r$ $d i s t i n c t p o i n t s o n a c i r c l e o f r a d i u s$ $i s 4 u n i t s t h e n a b c d i s e q u a l t o ?$

Question Number 31543 Answers: 0 Comments: 2

∫((x^3 +x+1)/(x^2 +1)) dx

$\int \frac{x^{3} + x + 1}{x^{2} + 1} d x$

Question Number 31502 Answers: 0 Comments: 3

find f(x)= ∫_0 ^1 ln(1+xt^2 )dt with x>0. 2) give thevalue of ∫_0 ^1 ln(1+t^2 )dt and ∫_0 ^1 ln(1+2t^2 )dt.

$f i n d f (x) = \int_{0}^{1} l n (1 + {x t}^{2}) d t w i t h x > 0 .$ $2) g i v e t h e v a l u e o f \int_{0}^{1} l n (1 + t^{2}) d t a n d \int_{0}^{1} l n (1 + 2 t^{2}) d t .$

Question Number 31369 Answers: 0 Comments: 0

Question Number 31340 Answers: 0 Comments: 0

Deduce the power series of sin^2 x. Hence show that if x is small then (sin^2 x − x^2 cosx)/x^4 =(1/6) − (x^2 /(360))

$D e d u c e t h e p o w e r s e r i e s o f {s i n}^{2} x .$ $H e n c e s h o w t h a t i f x i s s m a l l t h e n$ $({s i n}^{2} x - x^{2} c o s x) / x^{4} = \frac{1}{6} - \frac{x^{2}}{360}$

Question Number 31314 Answers: 0 Comments: 0

let x={(1/n)}_(n=1) ^∞ and y={(1/(n+1))}_(n=1) ^∞ be a sequence of real numbers and l_(2 ) ={x=(x_1 ,x_2 ,x_3 ,...):Σ_(n=1) ^∞ ∣xi∣^2 <∞} a linear space. (1) verify that x and y are in l_2 . (2) compute the inner product of x and y on l_2 please help me solve this question.

$l e t x = {\frac{1}{n}}_{n = 1}^{\infty} a n d y = {\frac{1}{n + 1}}_{n = 1}^{\infty} b e$ $a s e q u e n c e o f r e a l n u m b e r s a n d$ $l_{2} = {x = (x_{1}, x_{2}, x_{3}, . . .) : \underset{n = 1}{\sum^{\infty}} ∣ x i ∣^{2} < \infty}$ $a l i n e a r s p a c e .$ $(1) v e r i f y t h a t x a n d y a r e i n l_{2} .$ $(2) c o m p u t e t h e i n n e r p r o d u c t o f x$ $a n d y o n l_{2}$ $p l e a s e h e l p m e s o l v e t h i s$ $q u e s t i o n .$

Question Number 31306 Answers: 1 Comments: 0

Complete the square in y^2 +8y+9k and hence find the value of k that makes it a perfect square.

$Complete the square in y^{2} + 8 y + 9 k and hence find the$ $value of k that makes it a perfect square .$

Question Number 31281 Answers: 1 Comments: 0

find three nos in AP whose product is equal to the square of their sum.

$f i n d t h r e e n o s i n A P w h o s e p r o d u c t$ $i s e q u a l t o t h e s q u a r e o f t h e i r s u m .$

Question Number 31085 Answers: 0 Comments: 1

calculate ∫∫_(x^2 +y^2 −2x≤0) xdxdy.

$c a l c u l a t e \int \int_{x^{2} + y^{2} - 2 x ⩽ 0} x d x d y .$

Question Number 31017 Answers: 1 Comments: 0

solve (√(1+tan^2 x/1+cot^2 x= tanx))

$s o l v e \sqrt{1 + {t a n}^{2} x / 1 + {c o t}^{2} x = t a n x}$

Question Number 30771 Answers: 0 Comments: 0

let I_n = ∫_0 ^(π/4) (dx/(cos^(2n+1) )) (n∈N) 1) find a and b fromR /∀x∈[0,(π/4)] (1/(cosx))=((acosx)/(1−sinx)) +((bcosx)/(1+sinx)) .find I_0 2) verify the relation (1/(cos^(2n+3) x))=(1/(cos^(2n+1) x)) +((sinx sinx)/(cos^(2n+3) )) .find the relation of recurrence between I_n and I_(n+1) .

$l e t I_{n} = \int_{0}^{\frac{π}{4}} \frac{d x}{{c o s}^{2 n + 1}} (n \in N)$ $1) f i n d a a n d b f r o m R / \forall x \in [0, \frac{π}{4}]$ $\frac{1}{c o s x} = \frac{a c o s x}{1 - s i n x} + \frac{b c o s x}{1 + s i n x} . f i n d I_{0}$ $2) v e r i f y t h e r e l a t i o n$ $\frac{1}{{c o s}^{2 n + 3} x} = \frac{1}{{c o s}^{2 n + 1} x} + \frac{s i n x s i n x}{{c o s}^{2 n + 3}} . f i n d t h e r e l a t i o n$ $o f r e c u r r e n c e b e t w e e n I_{n} a n d I_{n + 1} .$