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Question Number 55663 Answers: 2 Comments: 0

Question Number 55658 Answers: 1 Comments: 0

find the difference of the roots of the following quadratic equation (3+2(√(2 )))x^2 +(1+(√2))x =2

$$\mathrm{find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}\:}\right)\mathrm{x}^{\mathrm{2}} \:+\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\mathrm{x}\:=\mathrm{2} \\ $$

Question Number 55643 Answers: 0 Comments: 1

known function f diferensiable continues at [a, b] If f(a)=f(b)=0 and ∫_a ^b [f(x)]^2 dx=1 Prove that ∫_a ^b x^2 [f′(x)]^2 dx ≥(1/4)

$$\mathrm{known}\:\mathrm{function}\:{f} \\ $$$$\mathrm{diferensiable}\:\mathrm{continues}\:\mathrm{at}\:\left[{a},\:{b}\right] \\ $$$$\mathrm{If}\:{f}\left({a}\right)={f}\left({b}\right)=\mathrm{0} \\ $$$$\mathrm{and}\: \\ $$$$\int_{{a}} ^{{b}} \left[{f}\left({x}\right)\right]^{\mathrm{2}} {dx}=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\int_{{a}} ^{{b}} {x}^{\mathrm{2}} \left[{f}'\left({x}\right)\right]^{\mathrm{2}} \:{dx}\:\geqslant\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 55642 Answers: 0 Comments: 0

Prove the following statements: If for every n , f_n form ascend function and {f_n } uniform convergences to f at [a, b], then lim_(n→∞) ∫_a ^b f_n (x) dx →∫_a ^b f(x) dx

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{statements}: \\ $$$$\mathrm{If}\:\mathrm{for}\:\mathrm{every}\:{n}\:,\:{f}_{{n}} \:\mathrm{form}\:\mathrm{ascend}\:\mathrm{function} \\ $$$$\mathrm{and}\:\left\{{f}_{{n}} \right\}\:\mathrm{uniform}\:\mathrm{convergences} \\ $$$$\mathrm{to}\:{f}\:\mathrm{at}\:\left[{a},\:{b}\right],\:\mathrm{then} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{{a}} ^{{b}} {f}_{{n}} \left({x}\right)\:{dx}\:\rightarrow\int_{{a}} ^{{b}} {f}\left({x}\right)\:{dx} \\ $$

Question Number 55641 Answers: 0 Comments: 1

Studies of convergences the numbers real sequence {x_n }, with x_1 =1 and x_(n+1) =((x_n ^2 +2)/(2x_n )), n≥1

$$\mathrm{Studies}\:\mathrm{of}\:\mathrm{convergences} \\ $$$$\mathrm{the}\:\mathrm{numbers}\:\mathrm{real}\:\mathrm{sequence}\:\left\{{x}_{{n}} \right\}, \\ $$$$\mathrm{with}\:{x}_{\mathrm{1}} =\mathrm{1}\:\mathrm{and}\:{x}_{{n}+\mathrm{1}} =\frac{{x}_{{n}} ^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}_{{n}} },\:{n}\geqslant\mathrm{1} \\ $$$$ \\ $$$$ \\ $$

Question Number 55640 Answers: 0 Comments: 0

known real numbers sequence {a_n } and {b_n } both of them convergences to 0. If {b_n } monotonous descend and lim_(n→∞) ((a_(n+1) −a_n )/(b_(n+1) −b_n )) . then lim_(n→∞) (a_n /(2b_n ))=..

$$\mathrm{known}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{sequence} \\ $$$$\left\{{a}_{{n}} \right\}\:\mathrm{and}\:\left\{{b}_{{n}} \right\}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them} \\ $$$$\mathrm{convergences}\:\mathrm{to}\:\mathrm{0}. \\ $$$$\mathrm{If}\:\left\{{b}_{{n}} \right\}\:\mathrm{monotonous}\:\mathrm{descend} \\ $$$$\mathrm{and}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{a}_{{n}+\mathrm{1}} −{a}_{{n}} }{{b}_{{n}+\mathrm{1}} −{b}_{{n}} }\:. \\ $$$$\mathrm{then}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{a}_{{n}} }{\mathrm{2}{b}_{{n}} }=.. \\ $$

Question Number 55639 Answers: 1 Comments: 0

Known a ∈ R and function f : R→R satiesfied ∣xf(x)+a∣ < sin^2 (x−a). For all x ∈ R value of lim_(x→a) f(x) ..

$$\mathrm{Known}\:{a}\:\in\:\mathbb{R}\:\mathrm{and} \\ $$$$\mathrm{function}\:{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{satiesfied} \\ $$$$\mid{xf}\left({x}\right)+{a}\mid\:<\:\mathrm{sin}^{\mathrm{2}} \:\left({x}−{a}\right).\: \\ $$$$\mathrm{For}\:\mathrm{all}\:{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{f}\left({x}\right)\:.. \\ $$

Question Number 55638 Answers: 1 Comments: 0

For all n ∈ N f_n (x)= { ((((nx)/(2n−1)), x ∈ [0, ((2n−1)/n)])),((1 , x ∈[((2n−1)/n), 2])) :} then for n→∞ ∫_1 ^2 f_n (x) dx convergences to..

$$\mathrm{For}\:\mathrm{all}\:{n}\:\in\:\mathbb{N} \\ $$$${f}_{{n}} \left({x}\right)=\begin{cases}{\frac{{nx}}{\mathrm{2}{n}−\mathrm{1}},\:\:\:\:\:{x}\:\in\:\left[\mathrm{0},\:\frac{\mathrm{2}{n}−\mathrm{1}}{{n}}\right]}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:,\:\:\:\:\:\:{x}\:\in\left[\frac{\mathrm{2}{n}−\mathrm{1}}{{n}},\:\mathrm{2}\right]}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{for}\:{n}\rightarrow\infty \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} {f}_{{n}} \left({x}\right)\:{dx}\:\mathrm{convergences}\:\mathrm{to}.. \\ $$$$ \\ $$

Question Number 55637 Answers: 2 Comments: 0

Value of lim_(n→∞) n ∫_0 ^1 ((2x^n )/(x+x^(2n+1) )) dx=..

$$\mathrm{Value}\:\mathrm{of}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{2}{x}^{{n}} }{{x}+{x}^{\mathrm{2}{n}+\mathrm{1}} }\:{dx}=.. \\ $$

Question Number 55636 Answers: 0 Comments: 0

known function f:[−5, 4]→R continues, then E={x ∈ [−5, 4] : f(x)}, then closure from E is...

$$\mathrm{known}\:\mathrm{function}\:{f}:\left[−\mathrm{5},\:\mathrm{4}\right]\rightarrow\mathbb{R}\:\mathrm{continues}, \\ $$$$\mathrm{then}\:{E}=\left\{{x}\:\in\:\left[−\mathrm{5},\:\mathrm{4}\right]\::\:{f}\left({x}\right)\right\}, \\ $$$$\mathrm{then}\:\mathrm{closure}\:\mathrm{from}\:{E}\:\mathrm{is}... \\ $$

Question Number 55635 Answers: 1 Comments: 1

Series Σ_(n=1) ^(∞) (1/n^2 )=..

$$\mathrm{Series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\Sigma}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }=.. \\ $$

Question Number 55634 Answers: 1 Comments: 0

If lim_(x→c) ((a_0 +a_1 (x−c)+a_2 (x−c)^2 +...+a_n (x−c)^n )/((x−c)^n ))=0 then a_0 +a_1 +a_2 +..+a_n =..

$$\mathrm{If}\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\:\frac{{a}_{\mathrm{0}} +{a}_{\mathrm{1}} \left({x}−{c}\right)+{a}_{\mathrm{2}} \left({x}−{c}\right)^{\mathrm{2}} +...+{a}_{{n}} \left({x}−{c}\right)^{{n}} }{\left({x}−{c}\right)^{{n}} }=\mathrm{0} \\ $$$$\mathrm{then}\:{a}_{\mathrm{0}} +{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +..+{a}_{{n}} =.. \\ $$

Question Number 55633 Answers: 1 Comments: 0

Known set A⊆R not empty, If Sup A=Inf A, then set A is..

$$\mathrm{Known}\:\mathrm{set}\:{A}\subseteq\mathbb{R}\:\mathrm{not}\:\mathrm{empty}, \\ $$$$\mathrm{If}\:\mathrm{Sup}\:{A}=\mathrm{Inf}\:{A},\:\mathrm{then}\:\mathrm{set}\:{A}\:\mathrm{is}.. \\ $$

Question Number 55631 Answers: 1 Comments: 0

Question Number 55628 Answers: 2 Comments: 0

In an A.P, the sum of the first 50 terms is 6275. Write this A.P . knowing that the ratio is 5.

$${In}\:{an}\:{A}.{P},\:{the}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{50}\:{terms}\:{is}\:\mathrm{6275}.\:{Write}\:\:{this}\:{A}.{P}\:.\:{knowing}\:{that}\:{the}\:{ratio}\:{is}\:\mathrm{5}. \\ $$

Question Number 55625 Answers: 0 Comments: 3

Question Number 55621 Answers: 1 Comments: 0

The function pogof(x) = x^4 + 2x^3 + 2x^2 is divisible by the half of the function of p. Find g(x).

$$\mathrm{The}\:\mathrm{function}\:\:\:\mathrm{pogof}\left(\mathrm{x}\right)\:\:=\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{the}\:\:\mathrm{half}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{function}\:\mathrm{of}\:\:\mathrm{p}.\:\:\mathrm{Find}\:\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 55615 Answers: 1 Comments: 0

let F(α)=∫_α ^(1+α^2 ) ((sin(αx))/(1+αx^2 ))dx 1) calculate (dF/dα)(α) 2) calculate lim_(α→0) F(α)

$${let}\:{F}\left(\alpha\right)=\int_{\alpha} ^{\mathrm{1}+\alpha^{\mathrm{2}} } \:\:\frac{{sin}\left(\alpha{x}\right)}{\mathrm{1}+\alpha{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{dF}}{{d}\alpha}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:{lim}_{\alpha\rightarrow\mathrm{0}} \:\:{F}\left(\alpha\right) \\ $$

Question Number 55613 Answers: 0 Comments: 5

Question Number 55592 Answers: 2 Comments: 1

lim_(x→π/3) ((cos x−sin (π/6))/((π/6)−(x/2)))=..

$$\underset{{x}\rightarrow\pi/\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}−\mathrm{sin}\:\frac{\pi}{\mathrm{6}}}{\frac{\pi}{\mathrm{6}}−\frac{{x}}{\mathrm{2}}}=.. \\ $$

Question Number 55587 Answers: 2 Comments: 0

If 12% of a number is equal to s, what is the e% of s? A. ((es)/(12)) B. ((es)/(88)) C. ((12s)/e) D. ((12e)/s)

$$\mathrm{If}\:\mathrm{12\%}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{s}, \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:{e\%}\:\mathrm{of}\:{s}? \\ $$$$\mathrm{A}.\:\frac{{es}}{\mathrm{12}} \\ $$$$\mathrm{B}.\:\frac{{es}}{\mathrm{88}} \\ $$$$\mathrm{C}.\:\frac{\mathrm{12}{s}}{{e}} \\ $$$$\mathrm{D}.\:\frac{\mathrm{12}{e}}{{s}} \\ $$

Question Number 55583 Answers: 1 Comments: 0

Question Number 55606 Answers: 0 Comments: 0

Question Number 55597 Answers: 1 Comments: 0

(d^2 y/dx^2 )+6y((dy/dx))^2 =0 Please solve the differential eq.

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{6}{y}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${Please}\:{solve}\:{the}\:{differential}\:{eq}. \\ $$

Question Number 55571 Answers: 0 Comments: 1

let u_n = ∫_(π/(n+1)) ^(π/n) (√(tan(x)))dx with n≥3 1) calculate U_n interms of n and calculate lim_(n→+∞ ) U_n 2) find nature of the serie Σ_(n≥3) U_n

$${let}\:{u}_{{n}} =\:\int_{\frac{\pi}{{n}+\mathrm{1}}} ^{\frac{\pi}{{n}}} \sqrt{{tan}\left({x}\right)}{dx}\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n}\:\:\:{and}\:{calculate}\:{lim}_{{n}\rightarrow+\infty\:\:} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}\geqslant\mathrm{3}} \:{U}_{{n}} \\ $$

Question Number 55561 Answers: 0 Comments: 3

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