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Question Number 145660 Answers: 1 Comments: 0

Question Number 145652 Answers: 2 Comments: 0

Question Number 145646 Answers: 1 Comments: 0

Find the arc lenght of the function y^2 = (x^3 /a) where a is a constant for 0≤x≤((7a)/3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{y}^{\mathrm{2}} \:=\:\frac{{x}^{\mathrm{3}} }{{a}}\:\mathrm{where}\:{a}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{for} \\ $$$$\mathrm{0}\leqslant{x}\leqslant\frac{\mathrm{7}{a}}{\mathrm{3}} \\ $$

Question Number 145645 Answers: 0 Comments: 0

∫_0 ^a x^(−(x/a)) dx

$$\int_{\mathrm{0}} ^{{a}} {x}^{−\frac{{x}}{{a}}} {dx} \\ $$

Question Number 145641 Answers: 0 Comments: 0

Let g:R→R be given by g(x) = 3 + 4x .Prove by induction that, for all positive integers n, g^n (x) = (4^n −1) + 4^n (x). If for every positive integer k, we inteprete g^(−k) as the inverse of the function g^k .Prove that the above formula holds alsl for all negative integers n.

$$\mathrm{Let}\:\mathrm{g}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{given}\:\mathrm{by}\:\mathrm{g}\left({x}\right)\:=\:\mathrm{3}\:+\:\mathrm{4}{x}\:.\mathrm{Prove}\:\mathrm{by}\:\mathrm{induction} \\ $$$$\mathrm{that},\:\mathrm{for}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:{n},\: \\ $$$$\mathrm{g}^{{n}} \left({x}\right)\:=\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right)\:+\:\mathrm{4}^{{n}} \left({x}\right). \\ $$$$\mathrm{If}\:\mathrm{for}\:\mathrm{every}\:\mathrm{positive}\:\mathrm{integer}\:{k},\:\mathrm{we}\:\mathrm{inteprete}\:\mathrm{g}^{−{k}} \:\mathrm{as}\:\mathrm{the}\:\mathrm{inverse} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{g}^{{k}} .\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{above}\:\mathrm{formula}\:\mathrm{holds}\:\mathrm{alsl} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{negative}\:\mathrm{integers}\:{n}. \\ $$

Question Number 145620 Answers: 1 Comments: 0

(d/dx)(((x+((x+((x+...))^(1/3) ))^(1/3) ))^(1/3) )=?

$$\frac{{d}}{{dx}}\left(\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+\sqrt[{\mathrm{3}}]{{x}+...}}}\right)=? \\ $$

Question Number 145615 Answers: 0 Comments: 2

Let a,b,c > 0 and abc = 1. Prove that (a^3 /((a+1)^2 ))+(b^3 /((b+1)^2 ))+(c^3 /((c+1)^2 )) ≥((a+b+c)/4)

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{abc}\:=\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{3}} }{\left({a}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{b}^{\mathrm{3}} }{\left({b}+\mathrm{1}\right)^{\mathrm{2}} }+\frac{{c}^{\mathrm{3}} }{\left({c}+\mathrm{1}\right)^{\mathrm{2}} }\:\geqslant\frac{{a}+{b}+{c}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 145602 Answers: 5 Comments: 0

.....Advanced .........Calculus..... Q:: Find the value of :: determinant ((( i :: 𝛗 := ∫_0 ^( 1) Ln ( Γ ( 2 + x ) )dx = ? )),(( ii :: Ω := Σ_(n=1) ^∞ (( 1)/( n ( 2n + 3 ))) = ?))) .....m.n.july.1970..... ■

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\mathrm{Advanced}\:.........\mathrm{Calculus}..... \\ $$$$\:\:\:\mathrm{Q}::\:\:\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{array}{|c|c|}{\:{i}\:::\:\:\:\boldsymbol{\phi}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Ln}\:\left(\:\Gamma\:\left(\:\mathrm{2}\:+\:{x}\:\right)\:\right){dx}\:=\:?\:\:\:\:}\\{\:{ii}\:::\:\:\:\Omega\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{\:{n}\:\left(\:\mathrm{2}{n}\:+\:\mathrm{3}\:\right)}\:=\:?}\\\hline\end{array} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{m}.{n}.{july}.\mathrm{1970}.....\:\:\:\:\blacksquare \\ $$$$ \\ $$

Question Number 145626 Answers: 0 Comments: 2

Question Number 145588 Answers: 3 Comments: 0

Question Number 145583 Answers: 0 Comments: 0

une urne contient N boules dont M boules blanches et N−M boule noires on tire successivement et sans remise n boules de l′urne. soit A_i :′′prelever une boules noires au ieme tirage′′ calculer P(A_i )

$${une}\:{urne}\:{contient}\:{N}\:{boules}\:{dont} \\ $$$${M}\:{boules}\:{blanches}\:{et}\:{N}−{M}\:{boule}\:{noires} \\ $$$${on}\:{tire}\:{successivement}\:{et}\:{sans}\:{remise} \\ $$$${n}\:{boules}\:{de}\:{l}'{urne}. \\ $$$${soit}\:{A}_{{i}} :''{prelever}\:{une}\:{boules}\:{noires}\:{au}\:{ieme} \\ $$$${tirage}'' \\ $$$${calculer}\:{P}\left({A}_{{i}} \right) \\ $$

Question Number 145580 Answers: 0 Comments: 1