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Question Number 201347 Answers: 1 Comments: 0

Question Number 201346 Answers: 0 Comments: 0

Question Number 201343 Answers: 1 Comments: 0

Question Number 201341 Answers: 2 Comments: 0

if a>0 and m≥0 ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )^2 ))dx=?

$i f a > 0 a n d m ⩾ 0$ $\int_{0}^{\infty} \frac{c o s (m x)}{{(x^{2} + a^{2})}^{2}} d x = ?$

Question Number 201463 Answers: 1 Comments: 0

a = constant number: if ∫x ∙ f(x) dx = x^3 - x^2 + 4x - (a/5) find f(2) = ?

$a = constant number :$ $if \int x \cdot f (x) dx = x^{3} - x^{2} + 4 x - \frac{a}{5}$ $find f (2) = ?$

Question Number 201462 Answers: 1 Comments: 0

Find: ∫_0 ^( 𝛑) (√(1 - 4 sin^2 (x/2) cos^2 (x/2))) dx = ?

$Find :$ $\int_{0}^{π} \sqrt{1 - 4 \sin^{2} \frac{x}{2} \cos^{2} \frac{x}{2}} dx = ?$

Question Number 201456 Answers: 1 Comments: 0

Question Number 201460 Answers: 1 Comments: 0

Find the smallest positive period of the function: y = ∣ tan 2x ∣ + ∣ cot 2x ∣

$Find the smallest positive period of the$ $function :$ $y = ∣ \tan 2 x ∣ + ∣ \cot 2 x ∣$

Question Number 201332 Answers: 1 Comments: 0

calcul : 1. lim_(n→+∞ ) ((sin(n^2 )−cos(n^3 ))/n) 2. lim_(n→+∞) ^n (√(3−sin(n^2 ))) 3. lim_(n→+∞) (n/(n+1)) e^(i((nπ)/3))

$c a l c u l :$ $1 . {l i m}_{n \to + \infty} \frac{s i n (n^{2}) - c o s (n^{3})}{n}$ $2 . {l i m}_{n \to + \infty}^{n} \sqrt{3 - s i n (n^{2})}$ $3 . {l i m}_{n \to + \infty} \frac{n}{n + 1} e^{i \frac{n π}{3}}$

Question Number 201329 Answers: 1 Comments: 0

Question Number 201325 Answers: 1 Comments: 1

Question Number 201323 Answers: 0 Comments: 0

Question Number 201322 Answers: 1 Comments: 0

Question Number 201491 Answers: 6 Comments: 1

1. x^2 −1+((x^4 −x^2 ))^(1/3) =10x 2. (√(x−(1/x)))+(√(1−(1/x)))=x 3. (√(2x−(8/x)))+2(√(1−(2/x)))≥x 4. (√(x^2 +x))+(√(x+2))≥(√(3(x^2 −2x+2))) 5. ((√(x+5))−(√(x−3)))(1+(√(x^2 +2x−15)))≥8 6. x^2 +3x+1=(x+1)(√(x^2 +1)) 7. 2x^2 +3x+7=(x+5)(√(2x^2 +1))

$1 . x^{2} - 1 + \sqrt[3]{x^{4} - x^{2}} = 10 x$ $2 . \sqrt{x - \frac{1}{x}} + \sqrt{1 - \frac{1}{x}} = x$ $3 . \sqrt{2 x - \frac{8}{x}} + 2 \sqrt{1 - \frac{2}{x}} ⩾ x$ $4 . \sqrt{x^{2} + x} + \sqrt{x + 2} ⩾ \sqrt{3 (x^{2} - 2 x + 2)}$ $5 . (\sqrt{x + 5} - \sqrt{x - 3}) (1 + \sqrt{x^{2} + 2 x - 15}) ⩾ 8$ $6 . x^{2} + 3 x + 1 = (x + 1) \sqrt{x^{2} + 1}$ $7 . 2 x^{2} + 3 x + 7 = (x + 5) \sqrt{2 x^{2} + 1}$