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Question Number 35791 Answers: 1 Comments: 0

A 5100 cm^2 trapezium has the perpendicular distance between the two parallel sides 60 m. If one of the parallel sides be 40 m then find the length of the other parallel side.

$$\mathrm{A}\:\mathrm{5100}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{trapezium}\:\mathrm{has}\:\mathrm{the}\:\mathrm{perpendicular} \\ $$$$\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two}\:\mathrm{parallel}\:\mathrm{sides} \\ $$$$\mathrm{60}\:\mathrm{m}.\:\mathrm{If}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{sides}\:\mathrm{be}\:\mathrm{40}\:\mathrm{m}\: \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{parallel}\:\mathrm{side}. \\ $$

Question Number 35771 Answers: 0 Comments: 2

Question Number 35769 Answers: 2 Comments: 0

Question Number 35768 Answers: 0 Comments: 0

Question Number 35766 Answers: 0 Comments: 1

let f(x)=arctan(1+x) and f_n (x)= e^(−nx) 1) define fof_n (x) and f_n of(x) 2) study the nature of the series Σ_(n=0) ^(+∞) fof_n (x) and Σ_(n=0) ^∞ f_n of(x) .

$${let}\:{f}\left({x}\right)={arctan}\left(\mathrm{1}+{x}\right)\:\:{and}\:\:{f}_{{n}} \left({x}\right)=\:{e}^{−{nx}} \\ $$$$\left.\mathrm{1}\right)\:{define}\:{fof}_{{n}} \left({x}\right)\:{and}\:{f}_{{n}} {of}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{nature}\:{of}\:{the}\:{series}\:\sum_{{n}=\mathrm{0}} ^{+\infty} {fof}_{{n}} \left({x}\right) \\ $$$${and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{f}_{{n}} {of}\left({x}\right)\:. \\ $$

Question Number 35763 Answers: 1 Comments: 0

Question Number 35743 Answers: 1 Comments: 1

find x log(log2+log_2 (x+1))=0

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{{x}} \\ $$$$\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{log}}\mathrm{2}+\boldsymbol{\mathrm{log}}_{\mathrm{2}} \left(\boldsymbol{{x}}+\mathrm{1}\right)\right)=\mathrm{0} \\ $$

Question Number 35739 Answers: 1 Comments: 2

Question Number 35738 Answers: 2 Comments: 0

Given that ∫_0 ^k x^2 = 16 find the value of k

$$\:{Given}\:{that}\:\:\int_{\mathrm{0}} ^{{k}} {x}^{\mathrm{2}} =\:\mathrm{16} \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$

Question Number 35737 Answers: 0 Comments: 4

Question Number 35732 Answers: 1 Comments: 1

Question Number 35729 Answers: 1 Comments: 1

find the value of I =∫_0 ^π (dx/(2−cosx))

$${find}\:{the}\:{value}\:{of}\:\:\:{I}\:=\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{dx}}{\mathrm{2}−{cosx}} \\ $$

Question Number 35833 Answers: 1 Comments: 1

fond lim_(n→+∞) n^a {ln(1+e^(−n) ) −e^(−n) } with a>0

$${fond}\:{lim}_{{n}\rightarrow+\infty} \:\:{n}^{{a}} \:\:\left\{{ln}\left(\mathrm{1}+{e}^{−{n}} \right)\:−{e}^{−{n}} \right\}\:{with}\:{a}>\mathrm{0} \\ $$

Question Number 35727 Answers: 0 Comments: 1

find lim_(x→0) ((sin(shx) −sh(sinx))/x)

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{{sin}\left({shx}\right)\:−{sh}\left({sinx}\right)}{{x}} \\ $$

Question Number 35726 Answers: 1 Comments: 1

find lim_(x→0) ((1−cos(sinx))/x^2 )

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

Question Number 35723 Answers: 1 Comments: 0

Find the largest prime factor of the following: (1×2×3)+(2×3×4)+...+(2014×2015×2016)

$${Find}\:{the}\:{largest}\:{prime}\:{factor}\:{of}\:\:{the}\:{following}: \\ $$$$\left(\mathrm{1}×\mathrm{2}×\mathrm{3}\right)+\left(\mathrm{2}×\mathrm{3}×\mathrm{4}\right)+...+\left(\mathrm{2014}×\mathrm{2015}×\mathrm{2016}\right) \\ $$

Question Number 35715 Answers: 1 Comments: 1

Find lim_(n→∞) ((3^(n+1) +2^(n+1) )/(3^n +2^n ))

$${Find}\underset{{n}\rightarrow\infty} {\:{lim}}\frac{\mathrm{3}^{{n}+\mathrm{1}} +\mathrm{2}^{{n}+\mathrm{1}} }{\mathrm{3}^{{n}} +\mathrm{2}^{{n}} } \\ $$

Question Number 35750 Answers: 0 Comments: 4

Question Number 35736 Answers: 1 Comments: 0

lim_(x→0) ((ln (sec (ex)sec (e^2 x)......sec (e^(50) x)))/(e^2 −e^(2cos x) )) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{sec}\:\left({ex}\right)\mathrm{sec}\:\left({e}^{\mathrm{2}} {x}\right)......\mathrm{sec}\:\left({e}^{\mathrm{50}} {x}\right)\right)}{{e}^{\mathrm{2}} −{e}^{\mathrm{2cos}\:{x}} }\:=\:? \\ $$

Question Number 35703 Answers: 1 Comments: 0

Question Number 35696 Answers: 0 Comments: 7

Question Number 35851 Answers: 1 Comments: 1

Question Number 35691 Answers: 0 Comments: 0

calculate lim_(a→0^+ ) ∫_(−a) ^a (√((1+x^2 )/(a^2 −x^2 ))) dx .

$${calculate}\:{lim}_{{a}\rightarrow\mathrm{0}^{+} \:\:\:\:} \:\:\:\int_{−{a}} ^{{a}} \:\:\sqrt{\frac{\mathrm{1}+{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} \:−{x}^{\mathrm{2}} }}\:\:{dx}\:. \\ $$

Question Number 35690 Answers: 0 Comments: 0

let B_n =Σ_(k=1) ^n sin(((kπ)/n)) sin((k/n^2 )) find lim_(n→+∞) B_n

$${let}\:{B}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{n}} \:\:{sin}\left(\frac{{k}\pi}{{n}}\right)\:{sin}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right) \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:{B}_{{n}} \\ $$

Question Number 35689 Answers: 1 Comments: 2

let S_n = Σ_(k=1) ^n (k^2 /(n^2 (√(n^2 +k^2 )))) find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} \sqrt{{n}^{\mathrm{2}} \:+{k}^{\mathrm{2}} }} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$

Question Number 35688 Answers: 1 Comments: 1

let A_n =Σ_(k=1) ^n (1/(k+n))ln(1+(k/n)) calculate lim_(n→+∞) A_n

$${let}\:{A}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{\mathrm{1}}{{k}+{n}}{ln}\left(\mathrm{1}+\frac{{k}}{{n}}\right) \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} {A}_{{n}} \\ $$

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