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AllQuestion and Answers: Page 1638

Question Number 39104 Answers: 1 Comments: 1

Question Number 39089 Answers: 2 Comments: 1

Question Number 39078 Answers: 1 Comments: 2

Without using l′hopital find lim_(x→3) ((√(9−x^2 ))/(x−3))

$W i t h o u t u s i n g l^{'} h o p i t a l$ $f i n d \lim_{x \to 3} \frac{\sqrt{9 - x^{2}}}{x - 3}$

Question Number 39072 Answers: 2 Comments: 1

Question Number 39067 Answers: 2 Comments: 7

Question Number 39059 Answers: 1 Comments: 0

Question Number 39058 Answers: 1 Comments: 1

Question Number 39055 Answers: 1 Comments: 0

Question Number 39040 Answers: 0 Comments: 0

find F(x) = ∫_0 ^π ln(x^2 −2x sin(2θ) +1)dθ .

$f i n d F (x) = \int_{0}^{π} l n (x^{2} - 2 x s i n (2 θ) + 1) d θ .$

Question Number 39039 Answers: 0 Comments: 2

let f(x) =(1/(1+∣sinx∣)) (2π periodic even) developp f at fourier serie .

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

Question Number 39038 Answers: 0 Comments: 2

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

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

Question Number 39037 Answers: 0 Comments: 2

calculate F(x)=∫_0 ^(2π) ((cos(4t))/(x^2 −2x cost +1)) dt

$c a l c u l a t e F (x) = \int_{0}^{2 π} \frac{c o s (4 t)}{x^{2} - 2 x c o s t + 1} d t$

Question Number 39035 Answers: 0 Comments: 1

find f(t) =∫_0 ^∞ sin(x)e^(−t [x]) dx with t>0

$f i n d f (t) = \int_{0}^{\infty} s i n (x) e^{- t [x]} d x w i t h t > 0$

Question Number 39034 Answers: 0 Comments: 1

calculate interms of n A_n = ∫_0 ^(2π) ((cos(nx))/(cosx +sinx))dx and B_n = ∫_0 ^(2π) ((sin(nx))/(cosx +sinx))dx .

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

Question Number 39033 Answers: 0 Comments: 2

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

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

Question Number 39032 Answers: 1 Comments: 0

x+y=3 x=2 y=?

$x + y = 3$ $x = 2$ $y = ?$

Question Number 39028 Answers: 1 Comments: 0

1) calculate A=cos((π/7)).cos(((2π)/7)).cos(((3π)/7)) 2) calculate B =tan((π/7)).tan(((2π)/7)).tan(((3π)/7)).

$1) c a l c u l a t e A = c o s (\frac{π}{7}) . c o s (\frac{2 π}{7}) . c o s (\frac{3 π}{7})$ $2) c a l c u l a t e B = t a n (\frac{π}{7}) . t a n (\frac{2 π}{7}) . t a n (\frac{3 π}{7}) .$

Question Number 39026 Answers: 2 Comments: 0

find the roots of 8x^3 −4x−1 =0

$f i n d t h e r o o t s o f 8 x^{3} - 4 x - 1 = 0$

Question Number 39025 Answers: 0 Comments: 1

let f(x)= ((cos(αx))/(cosx)) (2π periodic even) developp f at fourier serie.

$l e t f (x) = \frac{c o s (α x)}{c o s x} (2 π p e r i o d i c e v e n)$ $d e v e l o p p f a t f o u r i e r s e r i e .$

Question Number 39024 Answers: 0 Comments: 2

find the value of I = ∫_0 ^1 ((arctan(2x))/(√(1+4x^2 ))) dx

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

Question Number 39023 Answers: 0 Comments: 1

let g(x)= ∫_(−∞) ^(+∞) ((arctan(x(1+t^2 )))/(1+t^2 ))dt with x>0 find a simple form of g(x) .

$l e t g (x) = \int_{- \infty}^{+ \infty} \frac{a r c t a n (x (1 + t^{2}))}{1 + t^{2}} d t w i t h x > 0$ $f i n d a s i m p l e f o r m o f g (x) .$

Question Number 39022 Answers: 0 Comments: 1

let p(x)= (1+e^(iθ) x)^n −(1−e^(iθ) x)^n with n integr natural 1) find the roots of p(x) 2) fctorize inside C[x] p(x) 3) factorize inside R[x] p(x). θ ∈R

$l e t p (x) = {(1 + e^{i θ} x)}^{n} - {(1 - e^{i θ} x)}^{n} w i t h n i n t e g r n a t u r a l$ $1) f i n d t h e r o o t s o f p (x)$ $2) f c t o r i z e i n s i d e C [x] p (x)$ $3) f a c t o r i z e i n s i d e R [x] p (x) . θ \in R$

Question Number 39021 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^1 sin(narctanx)dx with n integr natural. 2) find nature of Σ_n A_n

$c a l c u l a t e A_{n} = \int_{0}^{1} s i n (n a r c t a n x) d x w i t h n i n t e g r n a t u r a l .$ $2) f i n d n a t u r e o f \sum_{n} A_{n}$

Question Number 39020 Answers: 1 Comments: 0

calculate ∫_0 ^1 ((ln(1+(√(x^2 +1))))/(√(x^2 +1))) dx

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

Question Number 39019 Answers: 1 Comments: 3

calculate ∫ (dx/((x^2 +1)(x^2 +2)(x^2 +3))) 1) find the value of ∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

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

Question Number 39018 Answers: 0 Comments: 0

find nature of Σ_(n=0) ^∞ (((−1)^([x]) )/(2+cos(n[x])))

$f i n d n a t u r e o f \sum_{n = 0}^{\infty} \frac{{(- 1)}^{[x]}}{2 + c o s (n [x])}$

Pg 1633 Pg 1634 Pg 1635 Pg 1636 Pg 1637 Pg 1638 Pg 1639 Pg 1640 Pg 1641 Pg 1642

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