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AllQuestion and Answers: Page 122

Question Number 204706 Answers: 0 Comments: 0

evaluate ∫_0 ^∞ 2^(−𝚪(x)) dx

$e v a l u a t e \int_{0}^{\infty} 2^{- Γ (x)} d x$

Question Number 204705 Answers: 0 Comments: 1

evalute ∫_0 ^∞ 2^(−(√(tanx))) dx

$e v a l u t e \int_{0}^{\infty} 2^{- \sqrt{t a n x}} d x$

Question Number 204702 Answers: 1 Comments: 0

prove that : cl(Q×Q )=^? R^2 note: (X ,d ) is a metric space , A ⊆ X : x∈ A^( −) =cl(A) ⇔ ∀ r >0 , B_r (x) ∩ A ≠ φ

$prove that :$ $cl (Q \times Q) \overset{?}{=} R^{2}$ $n o t e : (X, d) i s a m e t r i c s p a c e$ $, A \subseteq X : x \in \bar{A} = cl (A) \Leftrightarrow \forall r > 0, B_{r} (x) \cap A \neq ϕ$

Question Number 204701 Answers: 3 Comments: 0

Question Number 204717 Answers: 1 Comments: 0

((3^0 +3^1 +3^2 +.........+ 3^(200) )/(13)) =^(Remainder) ?

$\frac{3^{0} + 3^{1} + 3^{2} + . . . . . . . . . + 3^{200}}{13} \overset{Remainder}{=} ?$

Question Number 204691 Answers: 1 Comments: 0

(√(a÷(√(a÷(√(a÷∙∙∙÷(√a)))))))=?

$\sqrt{a \div \sqrt{a \div \sqrt{a \div \cdot \cdot \cdot \div \sqrt{a}}}} = ?$

Question Number 204690 Answers: 1 Comments: 0

((a^x ÷((b^y ÷(c^z )^(1/r) ))^(1/q) ))^(1/p) =?

$\sqrt[p]{a^{x} \div \sqrt[q]{b^{y} \div \sqrt[r]{c^{z}}}} = ?$

Question Number 204689 Answers: 1 Comments: 0

y=∣f(x)∣ ; (dy/dx)=?

$y =∣ f (x) ∣; \frac{d y}{d x} = ?$

Question Number 204688 Answers: 1 Comments: 0

f(x)=sgn(x); f^′ (x)=(d/dx)[f(x)]=?

$f (x) = s g n (x); f^{^{'}} (x) = \frac{d}{d x} [f (x)] = ?$

Question Number 204687 Answers: 0 Comments: 0

(√(a−(√(b−(√c)))))=?

$\sqrt{a - \sqrt{b - \sqrt{c}}} = ?$

Question Number 204684 Answers: 0 Comments: 2

Question Number 204674 Answers: 1 Comments: 1

Question Number 204671 Answers: 3 Comments: 0

if f(f(x))=x^2 −3x+4, find f(1)=?

$i f f (f (x)) = x^{2} - 3 x + 4, f i n d f (1) = ?$

Question Number 204666 Answers: 0 Comments: 0

this is a closed curve: f(θ)=(e^(iθ) )^((e^(iθ) )) =e^(−θsin θ) e^(iθcos θ) ; −π<θ≤π f: { ((x(θ)=e^(−θsin θ) cos (θcos θ))),((y(θ)=e^(−θsin θ) sin (θcos θ))) :} find the area

$this is a closed curve :$ $f (θ) = {(e^{i θ})}^{(e^{i θ})} = e^{- θ \sin θ} e^{i θ \cos θ}; - π < θ ⩽ π$ $f : {\begin{cases} x (θ) = e^{- θ \sin θ} \cos (θ \cos θ) \\ y (θ) = e^{- θ \sin θ} \sin (θ \cos θ) \end{cases}$ $find the area$

Question Number 204664 Answers: 2 Comments: 0

8+(√(8^2 +(√(8^4 +(√(8^8 +(√(8^(16) +(√(...)))))))))) = ?

$8 + \sqrt{8^{2} + \sqrt{8^{4} + \sqrt{8^{8} + \sqrt{8^{16} + \sqrt{. . .}}}}} = ?$

Question Number 204663 Answers: 1 Comments: 0

Question Number 204658 Answers: 2 Comments: 0

If a = (9)^(1/3) − (3)^(1/3) + 1 Find (((4 − a)/a))^6 = ?

$If a = \sqrt[3]{9} - \sqrt[3]{3} + 1$ $Find {(\frac{4 - a}{a})}^{6} = ?$

Question Number 204657 Answers: 1 Comments: 0

Consider point A inside a triangle with sides 3,4 and 5. if d is the sum of the distances of this point from the sides.what is the smallest value of d?

$C o n s i d e r p o i n t A i n s i d e a t r i a n g l e$ $w i t h s i d e s 3, 4 a n d 5 . i f d i s t h e s u m$ $o f t h e d i s t a n c e s o f t h i s p o i n t f r o m$ $t h e s i d e s . w h a t i s t h e s m a l l e s t$ $v a l u e o f d ?$

Question Number 204686 Answers: 0 Comments: 1

(√(a−(√(a−(√(a−∙∙∙))))))=?

$\sqrt{a - \sqrt{a - \sqrt{a - \cdot \cdot \cdot}}} = ?$

Question Number 204647 Answers: 4 Comments: 0

Question Number 204645 Answers: 1 Comments: 1

Let f : [ 1^ ∞) →R be a differentiable function such that f(1)= (1/3) and 3∫_1 ^x f(t) dt = x f(x)−(x^3 /3) ,x∈[1,∞) find tbe value of f(e)

$Let f : [\bar{1} \infty) \to R be a differentiable$ $function such that f (1) = \frac{1}{3} and$ $3 \underset{1}{\int^{x}} f (t) d t = x f (x) - \frac{x^{3}}{3}, x \in [1, \infty)$ $find tbe value of f (e)$

Question Number 204642 Answers: 1 Comments: 0

If (1/1^2 )+(1/2^2 )+(1/3^2 )+ (1/4^2 )+(1/5^2 ) + ............. = (π^2 /6) then (1/1^2 )+(1/3^2 )+(1/5^2 ) + ............. = ?

$If \frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}} + \frac{1}{5^{2}} + . . . . . . . . . . . . . = \frac{π^{2}}{6}$ $then \frac{1}{1^{2}} + \frac{1}{3^{2}} + \frac{1}{5^{2}} + . . . . . . . . . . . . . = ?$

Question Number 204640 Answers: 1 Comments: 0

f(x)=(1/( (√(1+x))))+(1/( (√(1+a))))+(√((ax)/(ax+8))) a>0 x>0 prove 1<f(x)<2

$f (x) = \frac{1}{\sqrt{1 + x}} + \frac{1}{\sqrt{1 + a}} + \sqrt{\frac{a x}{a x + 8}}$ $a > 0 x > 0$ $p r o v e 1 < f (x) < 2$

Question Number 204632 Answers: 3 Comments: 0

Question Number 204628 Answers: 2 Comments: 0

Question Number 204621 Answers: 3 Comments: 0

a , b , c ∈ R^+ If (√a) + (√b) + (√c) = 1 Prove that: a + b + c ≥ (1/3)

$a, b, c \in R^{+}$ $If \sqrt{a} + \sqrt{b} + \sqrt{c} = 1$ $Prove that : a + b + c ⩾ \frac{1}{3}$

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