Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1775

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 ?

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

Question Number 29464    Answers: 1   Comments: 0

An arrow is projected straight upwards at a speed of 100m/s. With what speed will it return to the ground if air resistance is ignored?

$${An}\:{arrow}\:{is}\:{projected}\:{straight} \\ $$$${upwards}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{100}{m}/{s}. \\ $$$${With}\:{what}\:{speed}\:{will}\:{it}\:{return}\:{to} \\ $$$${the}\:{ground}\:{if}\:{air}\:{resistance}\:{is} \\ $$$${ignored}? \\ $$

Question Number 29463    Answers: 1   Comments: 0

An object undergoes constant acceleration after starting from rest and then travels 5m in the first second.Determine how far it will go in the next second. a)15m b)10m c)20m d)5m

$${An}\:{object}\:{undergoes}\:{constant} \\ $$$${acceleration}\:{after}\:{starting}\:{from} \\ $$$${rest}\:{and}\:{then}\:{travels}\:\mathrm{5}{m}\:{in}\:{the} \\ $$$${first}\:{second}.{Determine}\:{how}\:{far} \\ $$$${it}\:{will}\:{go}\:{in}\:{the}\:{next}\:{second}. \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}{m}\:\:{b}\right)\mathrm{10}{m}\:{c}\right)\mathrm{20}{m}\:{d}\right)\mathrm{5}{m} \\ $$$$ \\ $$$$ \\ $$

Question Number 29461    Answers: 0   Comments: 1

let give u_n = (1/(√n))( (1/(√1)) +(1/(√2)) +...+(1/(√n))) find lim_(n→+∞) u_(n ) .

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

Question Number 29460    Answers: 2   Comments: 0

find lim_(x→0) ((e^(√(1+sinx)) −e)/(tanx)).

$${find}\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{e}^{\sqrt{\mathrm{1}+{sinx}}} \:\:−{e}}{{tanx}}. \\ $$

Question Number 29459    Answers: 0   Comments: 6

find lim_(x→0) (((sinx)/x))^(1/(1−cosx)) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\left(\frac{{sinx}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{1}−{cosx}}} \:. \\ $$

Question Number 29458    Answers: 0   Comments: 1

fimd lim_(x→0) ((((sinx)/(x(1+x)))−1+x)/x^2 ) .

$${fimd}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\frac{{sinx}}{{x}\left(\mathrm{1}+{x}\right)}−\mathrm{1}+{x}}{{x}^{\mathrm{2}} }\:. \\ $$

Question Number 29457    Answers: 0   Comments: 0

let give P_n (x)= Π_(k=1) ^n ch((x/2^(k)) )) find lim_(n→+∞) P_n (x) .

$${let}\:{give}\:{P}_{{n}} \left({x}\right)=\:\prod_{{k}=\mathrm{1}} ^{{n}} {ch}\left(\frac{{x}}{\mathrm{2}^{\left.{k}\right)} }\right)\: \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {P}_{{n}} \left({x}\right)\:. \\ $$

Question Number 29456    Answers: 0   Comments: 1

let give F(x)= ∫_x ^(2x) (dt/(√(1+t^2 +t^4 ))) 1) calculate (dF/dx)(x) 2)find lim_(x→+∞) F(x) and lim_(x→+∞) ((F(x))/x) .

$${let}\:{give}\:{F}\left({x}\right)=\:\int_{{x}} ^{\mathrm{2}{x}} \:\:\:\frac{{dt}}{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} +{t}^{\mathrm{4}} }}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{dF}}{{dx}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow+\infty} {F}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{F}\left({x}\right)}{{x}}\:. \\ $$

Question Number 29455    Answers: 1   Comments: 1

find ∫ 3^(√(2x+1)) dx .

$${find}\:\int\:\:\mathrm{3}^{\sqrt{\mathrm{2}{x}+\mathrm{1}}} \:{dx}\:. \\ $$

Question Number 29454    Answers: 0   Comments: 1

f is a function increasing and C^1 on [a,b] prove ∫_(f(a)) ^(f(b)) f^(−1) (t)dt = ∫_a ^b x f^′ (x)dx

$${f}\:{is}\:{a}\:{function}\:{increasing}\:{and}\:{C}^{\mathrm{1}} {on}\:\left[{a},{b}\right]\:{prove} \\ $$$$\:\int_{{f}\left({a}\right)} ^{{f}\left({b}\right)} \:{f}^{−\mathrm{1}} \left({t}\right){dt}\:=\:\int_{{a}} ^{{b}} \:{x}\:{f}^{'} \left({x}\right){dx}\: \\ $$

Question Number 29453    Answers: 0   Comments: 0

study and give the graph of the function f(x)= (x/(1+e^(−(1/x)) )) .

$${study}\:{and}\:{give}\:{the}\:{graph}\:{of}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:\:\:\:\frac{{x}}{\mathrm{1}+{e}^{−\frac{\mathrm{1}}{{x}}} }\:. \\ $$

Question Number 29452    Answers: 0   Comments: 1

find lim_(n→+∞) Π_(k=1) ^n (1 +(k/n))^(1/n) .

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\prod_{{k}=\mathrm{1}} ^{{n}} \:\:\left(\mathrm{1}\:+\frac{{k}}{{n}}\right)^{\frac{\mathrm{1}}{{n}}} \:\:. \\ $$

Question Number 29451    Answers: 0   Comments: 1

find ∫_0 ^(π/4) ln(1+tanx)dx .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{ln}\left(\mathrm{1}+{tanx}\right){dx}\:. \\ $$

Question Number 29450    Answers: 0   Comments: 1

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

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

Question Number 29449    Answers: 0   Comments: 0

find lim_(n→+∞) ^ ^n (√(n!)) .n^(−(n+1)) .

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

Question Number 29448    Answers: 0   Comments: 0

find lim_(x→1) ∫_x ^x^2 ((cos(πt))/(ln(t)))dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{cos}\left(\pi{t}\right)}{{ln}\left({t}\right)}{dt}\:. \\ $$

Question Number 29447    Answers: 0   Comments: 0

find A_n = ∫_0 ^∞ (dx/((1+x^2 )^n )) with n from N^★ .

$${find}\:\:\:{A}_{{n}} =\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

Question Number 29446    Answers: 1   Comments: 1

let give a<1 find the value of f(a)= ∫_0 ^(π/2) (dx/(1−acos^2 x)).

$${let}\:{give}\:{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}−{acos}^{\mathrm{2}} {x}}. \\ $$

Question Number 29445    Answers: 1   Comments: 0

find ∫ (dx/(sinx +sin(2x))) .

$${find}\:\:\:\int\:\:\:\:\:\:\:\frac{{dx}}{{sinx}\:+{sin}\left(\mathrm{2}{x}\right)}\:. \\ $$

  Pg 1770      Pg 1771      Pg 1772      Pg 1773      Pg 1774      Pg 1775      Pg 1776      Pg 1777      Pg 1778      Pg 1779   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com