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Question Number 65951 Answers: 0 Comments: 1

Question Number 65901 Answers: 1 Comments: 0

Question Number 65869 Answers: 1 Comments: 1

∫((2x^2 −3x+4)/(4x^3 +5)) dx

$\int \frac{2 x^{2} - 3 x + 4}{4 x^{3} + 5} d x$

Question Number 65841 Answers: 1 Comments: 1

(d/dx)(((tan^2 x)/(1 + cos x))) =?

$\frac{d}{d x} (\frac{t a n^{2} x}{1 + c o s x}) = ?$

Question Number 65782 Answers: 0 Comments: 4

Evaluate ∫_0 ^2 (3x^2 −2x + 4)^7 dx hence show that (d/dx)(coshx) = sinh x

$E v a l u a t e \int_{0}^{2} {(3 x^{2} - 2 x + 4)}^{7} d x$ $h e n c e s h o w t h a t \frac{d}{d x} (c o s h x) = s i n h x$

Question Number 65735 Answers: 0 Comments: 0

show that the maping define by (x y)=Σxy^ is an inner product

$s h o w t h a t t h e m a p i n g d e f i n e b y$ $(x y) = Σ x \bar{y}$ $i s a n i n n e r p r o d u c t$

Question Number 65601 Answers: 0 Comments: 1

1.If y=x^(n−1) log x,then prove that,x^2 (d^2 y/dx^2 )+(3−2n)x(dy/dx)+(n−1)^2 y=0 2.If ((mtan (α−θ))/(cos^2 θ))=((ntan θ)/(cos^2 (α−θ))),then prove that,θ=(1/2)[α−tan^(−1) (((n−m)/(n+m))tan α)]

$1 . If y = x^{n - 1} \log x, then prove that, x^{2} \frac{d^{2} y}{{d x}^{2}} + (3 - 2 n) x \frac{d y}{d x} + {(n - 1)}^{2} y = 0$ $2 . I f \frac{mtan (α - θ)}{\cos^{2} θ} = \frac{n \tan θ}{\cos^{2} (α - θ)}, then prove that, θ = \frac{1}{2} [α - \tan^{- 1} (\frac{n - m}{n + m} \tan α)]$

Question Number 65593 Answers: 1 Comments: 5

∫_0 ^(1/3) (3x + 1)^5 dx =

$\int_{0}^{\frac{1}{3}} {(3 x + 1)}^{5} d x =$

Question Number 65592 Answers: 1 Comments: 0

∫_0 ^(1/3) (3x + 1)^5 dx =

$\int_{0}^{\frac{1}{3}} {(3 x + 1)}^{5} d x =$

Question Number 65407 Answers: 0 Comments: 1

Question Number 65239 Answers: 1 Comments: 8

Question Number 65217 Answers: 0 Comments: 1

Question Number 65170 Answers: 0 Comments: 0

three forces F_1 , F_2 and F_3 acts through the points with position vectors r_1 ,r_2 and r_3 respectively where F_1 =(3i −2j−4k)N, r_1 = (i +k)m F_2 =(−i+j)N, r_2 =(j+k)m F_3 =(−i+4k)N, r_3 =(i+j+k)m a. show that this system does not reduce to a single force. When a fourth force F is added, the system of forces is in equilibrium b. Show that F acts through the point with vectors (3k)m.

$t h r e e f o r c e s F_{1}, F_{2} a n d F_{3} a c t s t h r o u g h t h e p o i n t s w i t h p o s i t i o n v e c t o r s$ $r_{1}, r_{2} a n d r_{3} r e s p e c t i v e l y w h e r e$ $F_{1} = (3 i - 2 j - 4 k) N, r_{1} = (i + k) m$ $F_{2} = (- i + j) N, r_{2} = (j + k) m$ $F_{3} = (- i + 4 k) N, r_{3} = (i + j + k) m$ $a . s h o w t h a t t h i s s y s t e m d o e s n o t r e d u c e t o a s i n g l e f o r c e .$ $W h e n a f o u r t h f o r c e F i s a d d e d, t h e s y s t e m o f f o r c e s i s i n e q u i l i b r i u m$ $b . S h o w t h a t F a c t s t h r o u g h t h e p o i n t w i t h v e c t o r s (3 k) m .$

Question Number 65168 Answers: 2 Comments: 0

z = 1− i(√3) express z in the form r(cosθ +isinθ) also express z^7 in the form re^(iθ) .

$z = 1 - i \sqrt{3}$ $e x p r e s s z i n t h e f o r m r (c o s θ + i s i n θ) a l s o e x p r e s s z^{7} i n t h e f o r m$ ${r e}^{i θ} .$

Question Number 65166 Answers: 2 Comments: 1

Given that f(x) = (2/(x^2 −1)) a) Express f(x) in partial fraction. b.Evaluate ∫_3 ^5 f (x) dx

$G i v e n t h a t f (x) = \frac{2}{x^{2} - 1}$ $a) E x p r e s s f (x) i n p a r t i a l f r a c t i o n .$ $b . E v a l u a t e \int_{3}^{5} f (x) d x$

Question Number 65113 Answers: 0 Comments: 1

Question Number 65052 Answers: 4 Comments: 0

A.Evaluate: (i)∫((sin x+cos x)/(9+16sin 2x))dx (ii)∫((1+x^2 )/((1−x^2 )(√(1+x^2 +x^4 ))))dx (iii)∫((x−1)/((x+1)(√(x^3 +x+x^2 ))))dx

$A . Evaluate :$ $(i) \int \frac{\sin x + \cos x}{9 + 16 \sin 2 x} d x$ $(ii) \int \frac{1 + x^{2}}{(1 - x^{2}) \sqrt{1 + x^{2} + x^{4}}} d x$ $(iii) \int \frac{x - 1}{(x + 1) \sqrt{x^{3} + x + x^{2}}} d x$

Question Number 65013 Answers: 1 Comments: 0

why do we divide each term by n when given the question lim_(x→∞) ((3 +2n)/(1+n)) ?

$w h y d o w e d i v i d e e a c h t e r m b y n w h e n g i v e n t h e q u e s t i o n$ $\lim_{x \to \infty} \frac{3 + 2 n}{1 + n} ?$

Question Number 65011 Answers: 5 Comments: 1

1.(i)Evaluate:∫(1/(sin x−cos x+(√2)))dx (ii)Evaluate:∫2^2^2^x 2^2^x 2^x dx (iii)Evaluate:∫((cos^3 x)/(sin^2 x+sin x))dx 2.cosec [tan^(−1) {cos (cot^(−1) (sec(sin^(−1) a)))}]=What? 3.Prove that, sin [cot^(−1) {cos (tan^(−1) x)}]=(√((x^2 +1)/(x^2 +2))) 4.Mention Order and Degree and state also if it is linear or non-linear. y+(d^2 y/dx^2 )=((19)/(25))∫y^2 dx

$1 . (i) Evaluate : \int \frac{1}{\sin x - \cos x + \sqrt{2}} d x$ $(ii) Evaluate : \int 2^{2^{2^{x}}} 2^{2^{x}} 2^{x} d x$ $(iii) Evaluate : \int \frac{\cos^{3} x}{\sin^{2} x + \sin x} d x$ $2 . cosec [\tan^{- 1} {\cos (\cot^{- 1} (\sec (\sin^{- 1} a)))}] = What ?$ $3 . Prove that, \sin [\cot^{- 1} {\cos (\tan^{- 1} x)}] = \sqrt{\frac{x^{2} + 1}{x^{2} + 2}}$ $4 . Mention Order and Degree and state also if it is linear or non - l inear .$ $y + \frac{d^{2} y}{{d x}^{2}} = \frac{19}{25} \int y^{2} d x$

Question Number 64966 Answers: 0 Comments: 0

Question Number 64829 Answers: 2 Comments: 4

Question Number 64824 Answers: 0 Comments: 0

Question Number 64823 Answers: 0 Comments: 5

Question Number 64812 Answers: 0 Comments: 2

how do i prove by induction? please

$h o w d o i p r o v e b y i n d u c t i o n ?$ $p l e a s e$

Question Number 64804 Answers: 1 Comments: 0

∫_0 ^(+∞) e^(−x^2 ) dx

${\int^{+ \infty}}_{0} e^{- x^{2}} d x$

Question Number 64791 Answers: 0 Comments: 1

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