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AllQuestion and Answers: Page 1680

Question Number 35084 Answers: 1 Comments: 1

Question Number 35080 Answers: 2 Comments: 0

If (a/(b+c)) +(b/(c+a)) +(c/(a+b))=1 then prove that (a^2 /(b+c)) +(b^2 /(c+a)) +(c^2 /(a+b))=0

$I f \frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} = 1 t h e n p r o v e t h a t$ $\frac{a^{2}}{b + c} + \frac{b^{2}}{c + a} + \frac{c^{2}}{a + b} = 0$

Question Number 35072 Answers: 0 Comments: 2

An n-digit decimal number has been conveerted into octal number.Say it has m digits.What are possible minimum and maximum values of m in terms of n?

$An n - digit decimal number has been$ $conveerted into octal number . Say it$ $has m digits . What are possible minimum$ $and maximum values of m in terms of$ $n ?$

Question Number 35071 Answers: 1 Comments: 0

A 20-digit decimal number has been converted into octal system.Say it has n digits. What can be minimum and maximum possible values of n?

$A 20 - digit decimal number has been$ $converted into octal system . Say it has$ $n digits . What can be minimum and$ $maximum possible values of n ?$

Question Number 35062 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^∞ (dt/((t^4 +1)^n )) with n integr natural .

$c a l c u l a t e A_{n} = \int_{0}^{\infty} \frac{d t}{{(t^{4} + 1)}^{n}}$ $w i t h n i n t e g r n a t u r a l .$

Question Number 35061 Answers: 2 Comments: 1

find ∫_0 ^∞ ((x^2 +3)/((x^4 +1)^2 ))dx

$f i n d \int_{0}^{\infty} \frac{x^{2} + 3}{{(x^{4} + 1)}^{2}} d x$

Question Number 35060 Answers: 1 Comments: 1

calculate ∫_0 ^(π/4) sinx ln(cosx)dx

$c a l c u l a t e \int_{0}^{\frac{π}{4}} s i n x l n (c o s x) d x$

Question Number 35059 Answers: 2 Comments: 2

find ∫_0 ^π (dx/(cosx +sinx))

$f i n d \int_{0}^{π} \frac{d x}{c o s x + s i n x}$

Question Number 35058 Answers: 1 Comments: 1

find ∫_0 ^(π/4) (dt/((1+cos^2 t)^3 ))

$f i n d \int_{0}^{\frac{π}{4}} \frac{d t}{{(1 + {c o s}^{2} t)}^{3}}$

Question Number 35057 Answers: 0 Comments: 1

let u_n =((n/(n+1)))^(1/n) −1 find the nature of Σ_(n≥0) u_n

$l e t u_{n} = {(\frac{n}{n + 1})}^{\frac{1}{n}} - 1$ $f i n d t h e n a t u r e o f \sum_{n ⩾ 0} u_{n}$

Question Number 35056 Answers: 0 Comments: 2

let p(x)=(1+jx)^n −(1−jx)^n 1) find the roots of p(x) 2)factorize p(x) inside C[x] j =e^(i((2π)/3)) .

$l e t p (x) = {(1 + j x)}^{n} - {(1 - j x)}^{n}$ $1) f i n d t h e r o o t s o f p (x)$ $2) f a c t o r i z e p (x) i n s i d e C [x]$ $j = e^{i \frac{2 π}{3}} .$

Question Number 35055 Answers: 1 Comments: 2

calculate ∫_(−∞) ^(+∞) (dx/((1+x+x^2 )^3 ))

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{d x}{{(1 + x + x^{2})}^{3}}$

Question Number 35054 Answers: 0 Comments: 1

find ∫_0 ^(π/4) ((xdx)/(2 +cosx))

$f i n d \int_{0}^{\frac{π}{4}} \frac{x d x}{2 + c o s x}$

Question Number 35053 Answers: 0 Comments: 0

let v(x)=ln(1+x+x^2 ) developp f at integr serie.

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

Question Number 35052 Answers: 0 Comments: 1

let f(x) = (x/(x^2 +x−1)) developp f atintegr serie

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

Question Number 35051 Answers: 0 Comments: 1

calculate Σ_(n=0) ^∞ ((n+3)/(2n+1))x^n

$c a l c u l a t e \sum_{n = 0}^{\infty} \frac{n + 3}{2 n + 1} x^{n}$

Question Number 35050 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ (((−1)^n x^(2n+1) )/(4n^2 −1))

$c a l c u l a t e \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n} x^{2 n + 1}}{4 n^{2} - 1}$

Question Number 35049 Answers: 1 Comments: 1

let A_n = ∫_(1/n) ^n (1+(1/x^2 ))arctanx dx 1) calculate A_n 2) find lim_(n→+∞) A_n

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

Question Number 35048 Answers: 0 Comments: 0

find ∫ (dx/(cos(sinx)))

$f i n d \int \frac{d x}{c o s (s i n x)}$

Question Number 35046 Answers: 0 Comments: 0

find F(x)= ∫_0 ^π ln( 1+x sin^2 t)dt with ∣x∣<1 2) calculate ∫_0 ^π ln(1+(1/2)sin^2 t)dt

$f i n d F (x) = \int_{0}^{π} l n (1 + x {s i n}^{2} t) d t w i t h ∣ x ∣< 1$ $2) c a l c u l a t e \int_{0}^{π} l n (1 + \frac{1}{2} {s i n}^{2} t) d t$

Question Number 35045 Answers: 0 Comments: 0

find f(x)=∫_0 ^∞ ((arctan(xt))/(1+t^2 ))dt .

$f i n d f (x) = \int_{0}^{\infty} \frac{a r c t a n (x t)}{1 + t^{2}} d t .$

Question Number 35044 Answers: 1 Comments: 1

1)find ∫ (√(1+t^2 )) dt 2) calculate ∫_1 ^(√3) (√(1+t^2 )) dt

$1) f i n d \int \sqrt{1 + t^{2}} d t$ $2) c a l c u l a t e \int_{1}^{\sqrt{3}} \sqrt{1 + t^{2}} d t$

Question Number 35043 Answers: 1 Comments: 0

let t>0 and F(t) =∫_0 ^∞ ((sin(x^2 ) e^(−tx^2 ) )/x^2 )dx calculate (dF/dt)(t).

$l e t t > 0 a n d F (t) = \int_{0}^{\infty} \frac{s i n (x^{2}) e^{- {t x}^{2}}}{x^{2}} d x$ $c a l c u l a t e \frac{d F}{d t} (t) .$

Question Number 35041 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^∞ ((n+1)/(n^3 (n+1)^2 ))

$f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{n + 1}{n^{3} {(n + 1)}^{2}}$

Question Number 35040 Answers: 0 Comments: 0

find the value of Σ_(n=1) ^∞ (x^n /(n(n+1)(2n−1))) 2) find the value of Σ_(n=1) ^∞ (((−1)^n )/(2^n n(n+1)(2n−1)))

$f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{x^{n}}{n (n + 1) (2 n - 1)}$ $2) f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{2^{n} n (n + 1) (2 n - 1)}$

Question Number 35023 Answers: 1 Comments: 1

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