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AllQuestion and Answers: Page 1479

Question Number 57323 Answers: 0 Comments: 1

calculate ∫∫_D ((x+y)/(3+(√(x^2 +y^2 ))))dxdy with D={(x,y)∈R^2 /x^2 +y^2 ≤2 and x≥0 ,y≥0}

$c a l c u l a t e \int \int_{D} \frac{x + y}{3 + \sqrt{x^{2} + y^{2}}} d x d y$ $w i t h D = {(x, y) \in R^{2} / x^{2} + y^{2} ⩽ 2$ $a n d x ⩾ 0, y ⩾ 0}$

Question Number 57321 Answers: 1 Comments: 1

calculate ∫∫_D (x−y)(√(x^2 +y^2 ))dxdy with D ={ (x,y)∈R^2 /x^2 +y^2 ≤2 and x≥0}

$c a l c u l a t e \int \int_{D} (x - y) \sqrt{x^{2} + y^{2}} d x d y$ $w i t h D = {(x, y) \in R^{2} / x^{2} + y^{2} ⩽ 2 a n d x ⩾ 0}$

Question Number 57320 Answers: 1 Comments: 1

calculate ∫∫_D xy e^(−x^2 −y^2 ) dxdy with D={(x,y)∈R^2 / 0≤x≤2 and 1≤y≤3}

$c a l c u l a t e \int \int_{D} x y e^{- x^{2} - y^{2}} d x d y$ $w i t h D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ 2 a n d$ $1 ⩽ y ⩽ 3}$

Question Number 57319 Answers: 1 Comments: 1

calculate ∫∫_D e^(x−y) dxdy with D={(x,y)∈R^2 /∣x∣<1 and 0≤y≤1}

$c a l c u l a t e \int \int_{D} e^{x - y} d x d y$ $w i t h D = {(x, y) \in R^{2} / ∣ x ∣< 1 a n d 0 ⩽ y ⩽ 1}$

Question Number 57310 Answers: 0 Comments: 1

Question Number 57309 Answers: 0 Comments: 0

Question Number 57306 Answers: 1 Comments: 2

Question Number 57302 Answers: 1 Comments: 0

Question Number 57296 Answers: 1 Comments: 1

Question Number 57289 Answers: 0 Comments: 3

Tangents are drawn to x^2 +y^2 =16 from the point P(0,h).These tangents meet the x−axis at A and B. If area of ΔPAB is minimum then find value of h ?

$T a n g e n t s a r e d r a w n t o x^{2} + y^{2} = 16 f r o m$ $t h e p o i n t P (0, h) . T h e s e t a n g e n t s m e e t$ $t h e x - a x i s a t A a n d B . I f a r e a o f Δ P A B$ $i s m i n i m u m t h e n f i n d v a l u e o f h ?$

Question Number 57284 Answers: 1 Comments: 1

y is varies directly as the square of x and inversely as z. if x is inceased by 10% and z is decreased by 20%, find the percentage change in y.

$y i s v a r i e s d i r e c t l y a s t h e s q u a r e o f x a n d$ $i n v e r s e l y a s z .$ $i f x i s i n c e a s e d b y 10 % a n d z i s$ $d e c r e a s e d b y 20 %, f i n d t h e p e r c e n t a g e$ $c h a n g e i n y .$

Question Number 57283 Answers: 1 Comments: 1

Question Number 57269 Answers: 2 Comments: 6

If A>0,B>0, and A+B=(π/3) , then maximum value of tanAtanB is ?

$I f A > 0, B > 0, a n d A + B = \frac{π}{3}, t h e n$ $m a x i m u m v a l u e o f t a n A t a n B i s ?$

Question Number 57253 Answers: 0 Comments: 4

lim_(x→0) ((e^x + e^(−x) )/x)

$\lim_{x \to 0} \frac{e^{x} + e^{- x}}{x}$

Question Number 57251 Answers: 1 Comments: 0

Question Number 57245 Answers: 1 Comments: 0

((a^8 +a^4 +1)/(a^4 +a^2 +1))=?

$\frac{a^{8} + a^{4} + 1}{a^{4} + a^{2} + 1} = ?$

Question Number 57244 Answers: 0 Comments: 1

Question Number 57228 Answers: 0 Comments: 1

find f(x) =∫_1 ^2 ((ln(1+xt))/t^2 ) dt with x>0

$f i n d f (x) = \int_{1}^{2} \frac{l n (1 + x t)}{t^{2}} d t w i t h x > 0$

Question Number 57227 Answers: 0 Comments: 0

let f(α)=∫_0 ^1 ((arctan(αx))/(1+αx^2 )) dx with α real 1) find f(α) interms of α 2) find the values of ∫_0 ^1 ((arctan(2x))/(1+2x^2 )) dx and ∫_0 ^1 ((arctan(4x))/(1+4x^2 ))dx

$l e t f (α) = \int_{0}^{1} \frac{a r c t a n (α x)}{1 + α x^{2}} d x w i t h α r e a l$ $1) f i n d f (α) i n t e r m s o f α$ $2) f i n d t h e v a l u e s o f \int_{0}^{1} \frac{a r c t a n (2 x)}{1 + 2 x^{2}} d x a n d \int_{0}^{1} \frac{a r c t a n (4 x)}{1 + 4 x^{2}} d x$

Question Number 57226 Answers: 0 Comments: 0

calculate A_n =∫_0 ^1 x^n (√((1−x)/(1+x)))dx with n integr natural

$c a l c u l a t e A_{n} = \int_{0}^{1} x^{n} \sqrt{\frac{1 - x}{1 + x}} d x w i t h n i n t e g r n a t u r a l$

Question Number 57224 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((3t^2 −5t +1)/((t+1)(t+2)(2t+3)))dt

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{3 t^{2} - 5 t + 1}{(t + 1) (t + 2) (2 t + 3)} d t$

Question Number 57225 Answers: 0 Comments: 2

1)calculate f(a) =∫_0 ^a ((2x−1)/((x^2 −x+3)(x^2 +1)))dx 1) calculate f(1)and f(2)

$1) c a l c u l a t e f (a) = \int_{0}^{a} \frac{2 x - 1}{(x^{2} - x + 3) (x^{2} + 1)} d x$ $1) c a l c u l a t e f (1) a n d f (2)$

Question Number 57222 Answers: 1 Comments: 0

Express 5.27 in form of a series and show that is equal to 5 (5/(18))

$Express 5.27 in form of a series and show that is equal$ $to 5 \frac{5}{18}$

Question Number 57241 Answers: 1 Comments: 0

∫((×(√(x+1)))/(x+2))dx

$\int \frac{\times \sqrt{x + 1}}{x + 2} dx$

Question Number 57212 Answers: 1 Comments: 0

Question Number 57194 Answers: 0 Comments: 1

let A_n =∫_n ^n (([(√(x+1))]−[(√x)])/x) dx with n natural integr and n≥1 1) find A_n interms of n 2)find nature of the serie Σ A_n

$l e t A_{n} = \int_{n}^{n} \frac{[\sqrt{x + 1}] - [\sqrt{x}]}{x} d x w i t h n n a t u r a l i n t e g r a n d n ⩾ 1$ $1) f i n d A_{n} i n t e r m s o f n$ $2) f i n d n a t u r e o f t h e s e r i e Σ A_{n}$

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