Question and Answers Forum

AllQuestion and Answers: Page 1797

Question Number 29554 Answers: 0 Comments: 1

let give f(x)= x^2 cos((1/x^2 )) if x∈]0,1] but its derivative f^′ is not integrable on ]0,1].

$$\left.{l}\left.{et}\:{give}\:{f}\left({x}\right)=\:{x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:{if}\:{x}\in\right]\mathrm{0},\mathrm{1}\right]\:{but}\:{its}\:{derivative}\:{f}^{'} \\ $$$$\left.{i}\left.{s}\:{not}\:{integrable}\:{on}\:\right]\mathrm{0},\mathrm{1}\right]. \\ $$

Question Number 29553 Answers: 0 Comments: 0

let put I(x)= ∫_x ^(+∞) ((sin^3 t)/t^2 )dt with x>0 find lim_(x→0^+ ) I(x) 2) find ∫_0 ^∞ ((sin^3 t)/t^2 )dt .

$${let}\:{put}\:\:{I}\left({x}\right)=\:\int_{{x}} ^{+\infty} \:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{I}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}^{\mathrm{3}} {t}}{{t}^{\mathrm{2}} }{dt}\:. \\ $$

Question Number 29552 Answers: 1 Comments: 1

find ∫_0 ^∞ (((√(x+1)) −1)/(x(x+1)))dx .

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{{x}+\mathrm{1}}\:−\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)}{dx}\:. \\ $$

Question Number 29551 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((arctan(2x)−arctanx)/x)dx.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx}. \\ $$

Question Number 29550 Answers: 1 Comments: 0

Question Number 29541 Answers: 0 Comments: 4

Question Number 29536 Answers: 1 Comments: 5

Find eccentricity of the ellipse 7x^2 +7y^2 +2xy+10x−10y−7=0 ?

$${Find}\:{eccentricity}\:{of}\:{the}\:{ellipse} \\ $$$$\mathrm{7}{x}^{\mathrm{2}} +\mathrm{7}{y}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{10}{x}−\mathrm{10}{y}−\mathrm{7}=\mathrm{0}\:? \\ $$

Question Number 29522 Answers: 1 Comments: 7

Question Number 29520 Answers: 1 Comments: 0

to make an open fish tank a glass sheet of 2mm gauge is used .the outer length ,breadth and height are 60.4 , 40.4, 40.2 respectively .how much maximum volume of water will be contained in it ?

$$\mathrm{to}\:\mathrm{make}\:\mathrm{an}\:\mathrm{open}\:\mathrm{fish}\:\mathrm{tank}\:\mathrm{a}\:\mathrm{glass}\:\mathrm{sheet}\:\mathrm{of}\: \\ $$$$\mathrm{2mm}\:\mathrm{gauge}\:\mathrm{is}\:\mathrm{used}\:.\mathrm{the}\:\mathrm{outer}\:\mathrm{length} \\ $$$$,\mathrm{breadth}\:\mathrm{and}\:\mathrm{height}\:\mathrm{are}\:\mathrm{60}.\mathrm{4}\:,\:\mathrm{40}.\mathrm{4},\: \\ $$$$\mathrm{40}.\mathrm{2}\:\mathrm{respectively}\:.\mathrm{how}\:\mathrm{much}\:\mathrm{maximum} \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{water}\:\mathrm{will}\:\mathrm{be}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{it}\:? \\ $$$$ \\ $$

Question Number 29517 Answers: 0 Comments: 1

∫x^6 −1/x^2 +1

$$\int\mathrm{x}^{\mathrm{6}} −\mathrm{1}/\mathrm{x}^{\mathrm{2}} +\mathrm{1} \\ $$

Question Number 29511 Answers: 0 Comments: 1

find lim_(n→+∞) (((n!)^2 )/((2n)!)) .

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\:\frac{\left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}\:. \\ $$

Question Number 29510 Answers: 0 Comments: 1

let w_n = (1/n)( 1 +e^(1/n) +e^(2/n) + ... e^((n−1)/n) ) find lim_(n→+∞) w_n .

$${let}\:\:\:{w}_{{n}} =\:\frac{\mathrm{1}}{{n}}\left(\:\mathrm{1}\:+{e}^{\frac{\mathrm{1}}{{n}}} \:+{e}^{\frac{\mathrm{2}}{{n}}} \:+\:...\:{e}^{\frac{{n}−\mathrm{1}}{{n}}} \right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {w}_{{n}} . \\ $$

Question Number 29509 Answers: 0 Comments: 1

find lim_(n→+ ∞) ((n!)/2^(n−1) ) .

$${find}\:{lim}_{{n}\rightarrow+\:\infty} \:\:\:\:\frac{{n}!}{\mathrm{2}^{{n}−\mathrm{1}} }\:. \\ $$

Question Number 29508 Answers: 0 Comments: 0

x and y are elements from R wich verify (x+(√(x^2 +1)))(y +(√(y^2 +1)))= 1 find x+y .

$${x}\:{and}\:{y}\:{are}\:{elements}\:{from}\:{R}\:{wich}\:{verify} \\ $$$$\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)\left({y}\:+\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}\right)=\:\mathrm{1}\:\:{find}\:{x}+{y}\:. \\ $$

Question Number 29507 Answers: 0 Comments: 0

solve [(√x) ] −x+1=0

$${solve}\:\:\:\left[\sqrt{{x}}\:\right]\:−{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 29506 Answers: 0 Comments: 1

le give A_n = ∫_0 ^(π/2) ((sin((2n−1)x))/(sinx))dx and B_n =∫_0 ^(π/2) ((sin^2 (nx))/(sin^2 x))dx 1)calculate A_n 2)prove that B_(n+1) −B_n = A_(n+1) .then find B_n .

$${le}\:{give}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sin}\left(\left(\mathrm{2}{n}−\mathrm{1}\right){x}\right)}{{sinx}}{dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}^{\mathrm{2}} \left({nx}\right)}{{sin}^{\mathrm{2}} {x}}{dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{B}_{{n}+\mathrm{1}} −{B}_{{n}} =\:{A}_{{n}+\mathrm{1}} .{then}\:{find}\:{B}_{{n}} . \\ $$

Question Number 29505 Answers: 0 Comments: 3

let give u_n = Σ_(k=0) ^∞ (1/((k+1)^2 2^k )) find lim_(n→∞) u_n .

$${let}\:{give}\:{u}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}}{\left({k}+\mathrm{1}\right)^{\mathrm{2}} \:\mathrm{2}^{{k}} }\:\:{find}\:\:{lim}_{{n}\rightarrow\infty} {u}_{{n}} \:\:. \\ $$

Question Number 29503 Answers: 0 Comments: 0

let U_(n,p) = Σ_(k=1) ^n (1/((n+k)^(p+1) )) with n,p from N^★ 1) calculate lim_(n→+∞) U_(n,p) for p≥2 2)prove that U_(n,1) is convergent 3) let V_n = Σ_(k=1) ^n sin((1/((n+k)^2 ))) find lim_∞ V_n .

$${let}\:{U}_{{n},{p}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{\left({n}+{k}\right)^{{p}+\mathrm{1}} }\:{with}\:{n},{p}\:{from}\:{N}^{\bigstar} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{n}\rightarrow+\infty} {U}_{{n},{p}} \:{for}\:{p}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{U}_{{n},\mathrm{1}} \:{is}\:{convergent} \\ $$$$\left.\mathrm{3}\right)\:{let}\:{V}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{sin}\left(\frac{\mathrm{1}}{\left({n}+{k}\right)^{\mathrm{2}} }\right)\:{find}\:{lim}_{\infty} \:{V}_{{n}} \:. \\ $$

Question Number 29501 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ (1/(n^2 (n+1)^2 (n+2)^2 )).

$${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} \left({n}+\mathrm{2}\right)^{\mathrm{2}} }. \\ $$

Question Number 29500 Answers: 0 Comments: 1

nature of the sequence u_n = Σ_(k=2) ^n (((−1)^k )/(kln(k))) .

$${nature}\:{of}\:{the}\:{sequence}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{2}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{{kln}\left({k}\right)}\:. \\ $$

Question Number 29498 Answers: 1 Comments: 1

Question Number 29499 Answers: 0 Comments: 0

find lim_(n→+∞) ( (1/(√n)) + (1/(√(2n))) + (1/(√(3n))) +....+(1/(√n^2 )))

$${find}\:\:{lim}_{{n}\rightarrow+\infty} \left(\:\:\frac{\mathrm{1}}{\sqrt{{n}}}\:+\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}{n}}}\:+\:\frac{\mathrm{1}}{\sqrt{\mathrm{3}{n}}}\:+....+\frac{\mathrm{1}}{\sqrt{{n}^{\mathrm{2}} }}\right) \\ $$

Question Number 29491 Answers: 1 Comments: 0

If 4sinx.cosy+2sinx+2cosy+1=0 where x,y ∈ [0,2pie]. Find largest possible value of the sum (x+y).

$${If}\:\mathrm{4}{sinx}.{cosy}+\mathrm{2}{sinx}+\mathrm{2}{cosy}+\mathrm{1}=\mathrm{0} \\ $$$${where}\:{x},{y}\:\in\:\left[\mathrm{0},\mathrm{2}{pie}\right].\:{Find}\:{largest}\: \\ $$$${possible}\:{value}\:{of}\:{the}\:{sum}\:\left({x}+{y}\right). \\ $$

Question Number 29490 Answers: 1 Comments: 0

A gas expands according to the law PV=K (constant). Initialy, v=1000cubic metres and p=40N/m^2 . If the pressure is decreased at the rate of 5N/m^2 /min. find the rate at which the gas is expanding when its volume is 2000cubic metres.

$$\mathrm{A}\:\mathrm{gas}\:\mathrm{expands}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{law}\:\mathrm{PV}=\mathrm{K}\:\left(\mathrm{constant}\right). \\ $$$$\mathrm{Initialy},\:\boldsymbol{\mathrm{v}}=\mathrm{1000cubic}\:\mathrm{metres}\:\mathrm{and}\:\boldsymbol{\mathrm{p}}=\mathrm{40N}/\mathrm{m}^{\mathrm{2}} . \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{is}\:\mathrm{decreased}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{5N}/\mathrm{m}^{\mathrm{2}} /\mathrm{min}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{gas}\:\mathrm{is}\:\mathrm{expanding}\:\mathrm{when}\:\mathrm{its}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{2000cubic}\:\mathrm{metres}. \\ $$$$ \\ $$

Question Number 29488 Answers: 1 Comments: 4

Question Number 29478 Answers: 1 Comments: 0

the number of ordered pairs (x,y) of real numbers satisfying 4x^2 −4x+2=sin^2 y and x^2 +y^2 ≤ 3 is ?

$${the}\:{number}\:{of}\:{ordered}\:{pairs}\:\left({x},{y}\right) \\ $$$${of}\:{real}\:{numbers}\:{satisfying}\: \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}={sin}^{\mathrm{2}} {y} \\ $$$${and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:\mathrm{3}\:{is}\:? \\ $$

Pg 1792 Pg 1793 Pg 1794 Pg 1795 Pg 1796 Pg 1797 Pg 1798 Pg 1799 Pg 1800 Pg 1801

Contact: info@tinkutara.com