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Question Number 46705 Answers: 0 Comments: 0

calculate Σ_(k=0) ^n (1/(3k+1)) interms of H_n H_n =Σ_(k=1) ^n (1/k) .

$${calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{interms}\:{of}\:{H}_{{n}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:. \\ $$

Question Number 46697 Answers: 1 Comments: 0

Find the sum of the first nterms of the G.P 3+1+(1/3)+...and show that the sum cannot exceed (9/2) however great n may be.

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{first}\:{nterms}\: \\ $$$${of}\:{the}\:{G}.{P}\:\mathrm{3}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+...{and}\:{show}\:{that} \\ $$$${the}\:{sum}\:{cannot}\:{exceed}\:\frac{\mathrm{9}}{\mathrm{2}}\:{however} \\ $$$${great}\:{n}\:{may}\:{be}. \\ $$

Question Number 46694 Answers: 1 Comments: 0

(y′′y−(y′)^2 )e^((y′)/y) =y^2 not sure if it′s possible to solve this at all...

$$\left({y}''{y}−\left({y}'\right)^{\mathrm{2}} \right)\mathrm{e}^{\frac{{y}'}{{y}}} ={y}^{\mathrm{2}} \\ $$$$\mathrm{not}\:\mathrm{sure}\:\mathrm{if}\:\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{at}\:\mathrm{all}... \\ $$

Question Number 46686 Answers: 2 Comments: 1

Question Number 46681 Answers: 1 Comments: 2

Question Number 46680 Answers: 1 Comments: 0

Question Number 46674 Answers: 1 Comments: 0

why slope is represented by m

$${why}\:{slope}\:{is}\:{represented}\:{by}\:{m} \\ $$

Question Number 46673 Answers: 0 Comments: 5

Question Number 46667 Answers: 0 Comments: 1

integrate ln (cosx+sinx)dx

$${integrate}\:\mathrm{ln}\:\left({cosx}+{sinx}\right){dx} \\ $$

Question Number 46657 Answers: 1 Comments: 0

integrte sin^(−1) x

$${integrte}\:\mathrm{sin}^{−\mathrm{1}} {x} \\ $$

Question Number 46652 Answers: 1 Comments: 0

2(1/2)y+5(1/2)y−2=3 could you help me

$$\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}+\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{2}=\mathrm{3} \\ $$$$\mathrm{could}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 46651 Answers: 1 Comments: 0

3(8/(19))−2x=1(6/(19)) plz help me

$$\mathrm{3}\frac{\mathrm{8}}{\mathrm{19}}−\mathrm{2x}=\mathrm{1}\frac{\mathrm{6}}{\mathrm{19}} \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 46640 Answers: 0 Comments: 1

1≤n,m∈N. Prove that 3(m+n)+10ln (m!n!)≥6(√(mnH_m H_n )). (H_m =Σ_(i=1) ^m (1/i), H_n =Σ_(j=1) ^n (1/j))

$$\mathrm{1}\leqslant{n},{m}\in\mathbb{N}.\:{Prove}\:{that} \\ $$$$\mathrm{3}\left({m}+{n}\right)+\mathrm{10ln}\:\left({m}!{n}!\right)\geqslant\mathrm{6}\sqrt{{mnH}_{{m}} {H}_{{n}} }. \\ $$$$\left({H}_{{m}} =\underset{{i}=\mathrm{1}} {\overset{{m}} {\sum}}\frac{\mathrm{1}}{{i}},\:{H}_{{n}} =\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{j}}\right) \\ $$

Question Number 46639 Answers: 1 Comments: 2

Question Number 46641 Answers: 0 Comments: 1

Question Number 46637 Answers: 2 Comments: 3

Question Number 46636 Answers: 1 Comments: 0

tan θ=10tan60^°

$$\mathrm{tan}\:\theta=\mathrm{10tan60}^{°} \\ $$

Question Number 46631 Answers: 0 Comments: 1

Question Number 46629 Answers: 1 Comments: 0

An object is projected from a height of 80m above the ground with a velocity of 40m/s at an angle of 30 degree to the horizontal.What is the tume of flight?

$${An}\:{object}\:{is}\:{projected}\:{from}\:{a} \\ $$$${height}\:{of}\:\mathrm{80}{m}\:{above}\:{the}\:{ground} \\ $$$${with}\:{a}\:{velocity}\:{of}\:\mathrm{40}{m}/{s}\:{at}\:{an} \\ $$$${angle}\:{of}\:\mathrm{30}\:{degree}\:{to}\:{the} \\ $$$${horizontal}.{What}\:{is}\:{the}\:{tume}\:{of} \\ $$$${flight}? \\ $$

Question Number 46624 Answers: 1 Comments: 4

The value of k which minimizes F(k)= ∫_0 ^4 ∣x(4−x)−k∣dx = ?

$${The}\:{value}\:{of}\:{k}\:{which}\:{minimizes} \\ $$$${F}\left({k}\right)=\:\int_{\mathrm{0}} ^{\mathrm{4}} \mid{x}\left(\mathrm{4}−{x}\right)−{k}\mid{dx}\:=\:? \\ $$

Question Number 46617 Answers: 1 Comments: 1

calculate Σ_(n=1) ^∞ (1/(n(n+1)(n+2)(n+3)(n+4)(n+5)))

$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)\left({n}+\mathrm{4}\right)\left({n}+\mathrm{5}\right)} \\ $$

Question Number 46612 Answers: 1 Comments: 4

1) calculate I_n = ∫_0 ^∞ x^n e^((1−i)x) dx with n integr natural and i^2 =−1 2) find ∫_0 ^∞ x^(4k+3) xsinx dx .

$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:{x}^{{n}} \:{e}^{\left(\mathrm{1}−{i}\right){x}} {dx}\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{4}{k}+\mathrm{3}} \:{xsinx}\:{dx}\:. \\ $$

Question Number 46611 Answers: 2 Comments: 1

Question Number 46610 Answers: 0 Comments: 2

let f_n (x)=e^(−nx) −2e^(−2nx) with x from[0,+∞[ 1)calculate ∫_0 ^∞ f_n (x)dx and Σ_(n=0) ^∞ (∫_0 ^∞ f_n (x)dx) 2) find S(x)=Σ_(n=0) ^∞ f_n (x) and ∫_0 ^∞ S(x)dx

$${let}\:{f}_{{n}} \left({x}\right)={e}^{−{nx}} −\mathrm{2}{e}^{−\mathrm{2}{nx}} \:\:{with}\:{x}\:{from}\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$$\left.\mathrm{1}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right)\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{S}\left({x}\right){dx} \\ $$

Question Number 46609 Answers: 0 Comments: 1

solve x y^(′′) −e^(−x) y^′ =x sinx

$${solve}\:\:\:\:{x}\:{y}^{''} \:−{e}^{−{x}} {y}^{'} \:\:\:={x}\:{sinx} \\ $$

Question Number 46608 Answers: 0 Comments: 0

let the d.e xy^(′′) +(x^2 −x)y^′ +2y =0 find a solution developpable at integr serie.

$${let}\:{the}\:{d}.{e}\:\:{xy}^{''} \:+\left({x}^{\mathrm{2}} −{x}\right){y}^{'} \:+\mathrm{2}{y}\:=\mathrm{0} \\ $$$${find}\:{a}\:{solution}\:{developpable}\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$

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