Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 1682

Question Number 34901 Answers: 0 Comments: 3

∫_(−π/2) ^(+π/2) (√(cos^(2n−1) x−cos^(2n+1) x))dx =[−((2cos^((2n+1)/2) x)/(2n+1))]_(−π/2) ^(+π/2) =0? What is the mistake in above? ∫_(−π/2) ^(+π/2) (√(cos^(2n−1) x−cos^(2n+1) x))dx =2∫_0 ^(π/2) (√(cos^(2n−1) x−cos^(2n+1) x))dx =(4/(2n+1)) (this is correct answer)

$\int_{- π / 2}^{+ π / 2} \sqrt{\cos^{2 n - 1} x - \cos^{2 n + 1} x} d x$ $= {[- \frac{{2 \cos}^{\frac{2 n + 1}{2}} x}{2 n + 1}]}_{- π / 2}^{+ π / 2} = 0 ?$ $What is the mistake in above ?$ $\int_{- π / 2}^{+ π / 2} \sqrt{\cos^{2 n - 1} x - \cos^{2 n + 1} x} d x$ $= 2 \int_{0}^{π / 2} \sqrt{\cos^{2 n - 1} x - \cos^{2 n + 1} x} d x$ $= \frac{4}{2 n + 1} (this is correct answer)$

Question Number 34878 Answers: 1 Comments: 0

show that C_(n−1) ^(n+r−1) =C_r ^(n+r−1)

$s h o w t h a t$ ${\overset{n + r - 1}{C}}_{n - 1} = {\overset{n + r - 1}{C}}_{r}$

Question Number 34877 Answers: 2 Comments: 1

4 couples are to take a photograph with a newly wedded couple in a wedding party.In how many ways can this be done if: i)the celebrated couple must stand in the middle ii)each couple must stand next to each other iii)the celebrated couple must not stand next to each other

$4 c o u p l e s a r e t o t a k e a p h o t o g r a p h$ $w i t h a n e w l y w e d d e d c o u p l e i n a$ $w e d d i n g p a r t y . I n h o w m a n y w a y s$ $c a n t h i s b e d o n e i f :$ $i) t h e c e l e b r a t e d c o u p l e m u s t s t a n d$ $i n t h e m i d d l e$ $i i) e a c h c o u p l e m u s t s t a n d n e x t t o$ $e a c h o t h e r$ $i i i) t h e c e l e b r a t e d c o u p l e m u s t n o t$ $s t a n d n e x t t o e a c h o t h e r$

Question Number 34870 Answers: 3 Comments: 4

Question Number 34866 Answers: 0 Comments: 0

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

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

Question Number 34865 Answers: 0 Comments: 0

let f(x)= e^(−(√(1+2x))) developp f at integr serie .

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

Question Number 34864 Answers: 0 Comments: 0

let f(x)=x arctan(1+e^(−x) ) developp f at intrgr serie .

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

Question Number 34863 Answers: 0 Comments: 1

let f(x)= ((artan(x+1))/(1+2x)) developp f at integr serie .

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

Question Number 34862 Answers: 2 Comments: 8

find the value of f(x) = ∫_0 ^π ((cosx)/(1+2sin(2x)))dx

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

Question Number 34850 Answers: 2 Comments: 0

Question Number 34849 Answers: 0 Comments: 2

let f(x) = (e^(−x) /(2+x)) developp f at integr serie.

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

Question Number 34843 Answers: 0 Comments: 1

lim_ _(x→∞) ((ln x)/x) = ? You can only use series expansion / sandwich theorem!

$\underset{x \to \infty}{\lim_{}} \frac{\ln x}{x} = ?$ $Y o u c a n o n l y u s e$ $s e r i e s e x p a n s i o n / s a n d w i c h t h e o r e m!$

Question Number 34827 Answers: 1 Comments: 5

Find ∫ Sin^6 x dx

$F i n d \int {S i n}^{6} x d x$

Question Number 34821 Answers: 2 Comments: 1

Find range of y=(x/((x−1)(x−2))) .

$F i n d r a n g e o f$ $y = \frac{x}{(x - 1) (x - 2)} .$

Question Number 34792 Answers: 2 Comments: 0

solve for x 4x=2^x

$solve for x$ $4 x = 2^{x}$

Question Number 34845 Answers: 0 Comments: 0

f(x)=cos(x) g(x)=2^x f:R→R g:R→R^+ [f(x)]^2 +[f(π/2−x)]^2 =((log_2 g(x))/x);x≠0 f(g(x)x)=[f(g(x−1)x)]^2 +[f(π/2−g(x−1)x)]^2 find f and g

$f (x) = \cos (x)$ $g (x) = 2^{x}$ $f : R \to R$ $g : R \to R^{+}$ ${[f (x)]}^{2} + {[f (π / 2 - x)]}^{2} = \frac{\log_{2} g (x)}{x}; x \neq 0$ $f (g (x) x) = {[f (g (x - 1) x)]}^{2} + {[f (π / 2 - g (x - 1) x)]}^{2}$ $find f and g$

Question Number 34803 Answers: 1 Comments: 2

Question Number 34781 Answers: 1 Comments: 0

Question Number 34774 Answers: 1 Comments: 1

find lim_(n→+∞) ((n^p sin^2 (n!))/n^(p+1) ) with0<p<1 .

$f i n d {l i m}_{n \to + \infty} \frac{n^{p} {s i n}^{2} (n!)}{n^{p + 1}} w i t h 0 < p < 1 .$

Question Number 34771 Answers: 0 Comments: 1

let A(x)= ∫_0 ^1 ln(1+ix^2 )dx find a simple form of f(x) (x∈R)

$l e t A (x) = \int_{0}^{1} l n (1 + {i x}^{2}) d x$ $f i n d a s i m p l e f o r m o f f (x) (x \in R)$

Question Number 34770 Answers: 1 Comments: 2

let f(x)= ln(1+ix^2 ) 1) extrsct Re(f(x)) and Im(f(x)) 2) developp f at integr serie 3) calculate f^′ (x) by two methods

$l e t f (x) = l n (1 + {i x}^{2})$ $1) e x t r s c t R e (f (x)) a n d I m (f (x))$ $2) d e v e l o p p f a t i n t e g r s e r i e$ $3) c a l c u l a t e f^{^{'}} (x) b y t w o m e t h o d s$

Question Number 34765 Answers: 1 Comments: 0

Question Number 34762 Answers: 1 Comments: 0

Question Number 34760 Answers: 2 Comments: 0

Question Number 34759 Answers: 1 Comments: 0

Question Number 34755 Answers: 1 Comments: 5

lim_(x→0) ((1/x) − ((ln^(1000) (1 + x))/x^(1001) ))

$\lim_{x \to 0} (\frac{1}{x} - \frac{\ln^{1000} (1 + x)}{x^{1001}})$

Pg 1677 Pg 1678 Pg 1679 Pg 1680 Pg 1681 Pg 1682 Pg 1683 Pg 1684 Pg 1685 Pg 1686

Terms of Service

Contact: info@tinkutara.com