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AllQuestion and Answers: Page 1661

Question Number 35726 Answers: 1 Comments: 1

find lim_(x→0) ((1−cos(sinx))/x^2 )

$f i n d {l i m}_{x \to 0} \frac{1 - c o s (s i n x)}{x^{2}}$

Question Number 35723 Answers: 1 Comments: 0

Find the largest prime factor of the following: (1×2×3)+(2×3×4)+...+(2014×2015×2016)

$F i n d t h e l a r g e s t p r i m e f a c t o r o f t h e f o l l o w i n g :$ $(1 \times 2 \times 3) + (2 \times 3 \times 4) + . . . + (2014 \times 2015 \times 2016)$

Question Number 35715 Answers: 1 Comments: 1

Find lim_(n→∞) ((3^(n+1) +2^(n+1) )/(3^n +2^n ))

$F i n d \underset{n \to \infty}{l i m} \frac{3^{n + 1} + 2^{n + 1}}{3^{n} + 2^{n}}$

Question Number 35750 Answers: 0 Comments: 4

Question Number 35736 Answers: 1 Comments: 0

lim_(x→0) ((ln (sec (ex)sec (e^2 x)......sec (e^(50) x)))/(e^2 −e^(2cos x) )) = ?

$\lim_{x \to 0} \frac{\ln (\sec (e x) \sec (e^{2} x) . . . . . . \sec (e^{50} x))}{e^{2} - e^{2 \cos x}} = ?$

Question Number 35703 Answers: 1 Comments: 0

Question Number 35696 Answers: 0 Comments: 7

Question Number 35851 Answers: 1 Comments: 1

Question Number 35691 Answers: 0 Comments: 0

calculate lim_(a→0^+ ) ∫_(−a) ^a (√((1+x^2 )/(a^2 −x^2 ))) dx .

$c a l c u l a t e {l i m}_{a \to 0^{+}} \int_{- a}^{a} \sqrt{\frac{1 + x^{2}}{a^{2} - x^{2}}} d x .$

Question Number 35690 Answers: 0 Comments: 0

let B_n =Σ_(k=1) ^n sin(((kπ)/n)) sin((k/n^2 )) find lim_(n→+∞) B_n

$l e t B_{n} = \sum_{k = 1}^{n} s i n (\frac{k π}{n}) s i n (\frac{k}{n^{2}})$ $f i n d {l i m}_{n \to + \infty} B_{n}$

Question Number 35689 Answers: 1 Comments: 2

let S_n = Σ_(k=1) ^n (k^2 /(n^2 (√(n^2 +k^2 )))) find lim_(n→+∞) S_n

$l e t S_{n} = \sum_{k = 1}^{n} \frac{k^{2}}{n^{2} \sqrt{n^{2} + k^{2}}}$ $f i n d {l i m}_{n \to + \infty} S_{n}$

Question Number 35688 Answers: 1 Comments: 1

let A_n =Σ_(k=1) ^n (1/(k+n))ln(1+(k/n)) calculate lim_(n→+∞) A_n

$l e t A_{n} = \sum_{k = 1}^{n} \frac{1}{k + n} l n (1 + \frac{k}{n})$ $c a l c u l a t e {l i m}_{n \to + \infty} A_{n}$

Question Number 35687 Answers: 1 Comments: 2

calculate f(a)=∫_0 ^π (dx/(1−a cosx)) a from R . 2) application calculate ∫_0 ^π (dx/(1−2cosx))

$c a l c u l a t e f (a) = \int_{0}^{π} \frac{d x}{1 - a c o s x} a f r o m R .$ $2) a p p l i c a t i o n c a l c u l a t e \int_{0}^{π} \frac{d x}{1 - 2 c o s x}$

Question Number 35686 Answers: 1 Comments: 1

calculate ∫_(√3) ^(+∞) (dx/(x(√( 2+x^2 )))) .

$c a l c u l a t e \int_{\sqrt{3}}^{+ \infty} \frac{d x}{x \sqrt{2 + x^{2}}} .$

Question Number 35685 Answers: 1 Comments: 1

calculate ∫_0 ^(π/4) x artan(2x+1)dx

$c a l c u l a t e \int_{0}^{\frac{π}{4}} x a r t a n (2 x + 1) d x$

Question Number 35684 Answers: 1 Comments: 1

calculate I = ∫_0 ^1 e^(2t) ln(1+e^t )dt

$c a l c u l a t e I = \int_{0}^{1} e^{2 t} l n (1 + e^{t}) d t$

Question Number 35683 Answers: 1 Comments: 1

find ∫ x^2 ln(x^6 −1)dx

$f i n d \int x^{2} l n (x^{6} - 1) d x$

Question Number 35682 Answers: 1 Comments: 2

let F(x) = ∫_(x +1) ^(x^2 +1) arctan(1+t)dt 1) calculate (∂F/∂x)(x) 2) find lim_(x→0) F(x) .

$l e t F (x) = \int_{x + 1}^{x^{2} + 1} a r c t a n (1 + t) d t$ $1) c a l c u l a t e \frac{\partial F}{\partial x} (x)$ $2) f i n d {l i m}_{x \to 0} F (x) .$

Question Number 35681 Answers: 1 Comments: 1

find ∫ arctan(x)dx

$f i n d \int a r c t a n (x) d x$

Question Number 35680 Answers: 0 Comments: 0

by using residus theorem calculate W_n =∫_0 ^(π/2) cos^(2n) t dt ( wallis integal) n integr natural .

$b y u s i n g r e s i d u s t h e o r e m c a l c u l a t e$ $W_{n} = \int_{0}^{\frac{π}{2}} {c o s}^{2 n} t d t (w a l l i s i n t e g a l) n i n t e g r$ $n a t u r a l .$

Question Number 35678 Answers: 0 Comments: 1

let f(t) =∫_0 ^∞ ((e^(−tx^2 ) arctan(x^2 ))/x^2 )dx with t>0 1) study the existencte of f(t) 2)calculate f^′ (t) 3)find a simple form of f(t).

$l e t f (t) = \int_{0}^{\infty} \frac{e^{- {t x}^{2}} a r c t a n (x^{2})}{x^{2}} d x w i t h t > 0$ $1) s t u d y t h e e x i s t e n c t e o f f (t)$ $2) c a l c u l a t e f^{^{'}} (t)$ $3) f i n d a s i m p l e f o r m o f f (t) .$

Question Number 35677 Answers: 0 Comments: 2

find F(x)=∫_0 ^x e^(−2t) cos(t+(π/4))dx.

$f i n d F (x) = \int_{0}^{x} e^{- 2 t} c o s (t + \frac{π}{4}) d x .$

Question Number 35676 Answers: 0 Comments: 1

find f(x)=∫_0 ^x ch^4 t dt

$f i n d f (x) = \int_{0}^{x} {c h}^{4} t d t$

Question Number 35675 Answers: 0 Comments: 1

calculate ∫_1 ^3 (x/(e^x −1))dx ..

$c a l c u l a t e \int_{1}^{3} \frac{x}{e^{x} - 1} d x . .$

Question Number 35656 Answers: 0 Comments: 5

Following alphabet lacks one letter. abcdefghijklmnopqrstuvxyz I request that letter, please come and make the alphabet complete.

$Following alphabet lacks one letter .$ $abcdefghijklmnopqrstuvxyz$ $I request that letter,$ $please come and make the alphabet$ $complete .$

Question Number 35654 Answers: 1 Comments: 0

if cos^2 θ−sin^2 θ=tan^2 ∅ Then proof that 2cos^2 ∅−1=cos^2 ∅−sin^2 ∅=2tan^2 θ

$i f \cos^{2} θ - \sin^{2} θ = \tan^{2} \emptyset T h e n p r o o f t h a t$ $2 \cos^{2} \emptyset - 1 = \cos^{2} \emptyset - \sin^{2} \emptyset = 2 \tan^{2} θ$

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