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Question Number 159868 Answers: 1 Comments: 0

prove that ∫_(−∞) ^(+∞) δ(t)dt=1 δ(t) is dirac delta function (impluse function)

$${prove}\:{that} \\ $$$$\int_{−\infty} ^{+\infty} \delta\left({t}\right){dt}=\mathrm{1} \\ $$$$\delta\left({t}\right)\:{is}\:{dirac}\:{delta}\:{function}\:\left({impluse}\:{function}\right) \\ $$

Question Number 159982 Answers: 1 Comments: 0

(1+bf(x))f′′(x)=(p/(λa)) solve this equation: find f(x)

$$\left(\mathrm{1}+{bf}\left({x}\right)\right){f}''\left({x}\right)=\frac{{p}}{\lambda{a}} \\ $$$${solve}\:{this}\:{equation}:\:{find}\:\:{f}\left({x}\right) \\ $$

Question Number 159864 Answers: 2 Comments: 0

Question Number 159863 Answers: 1 Comments: 0

Dertermine all pairs (x;y) of integers such that 2010x - xy + 2012y + 1 = 0

$$\mathrm{Dertermine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}}\right)\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{2010x}\:-\:\mathrm{xy}\:+\:\mathrm{2012y}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 159860 Answers: 1 Comments: 1

Question Number 159857 Answers: 0 Comments: 0

Question Number 211805 Answers: 0 Comments: 0

Question Number 159854 Answers: 1 Comments: 0

Ω := ∫_0 ^( (π/4)) x.ln(sin(x))dx= ?

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {x}.{ln}\left({sin}\left({x}\right)\right){dx}=\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 159852 Answers: 2 Comments: 0

Question Number 159845 Answers: 2 Comments: 1

if q = 1−sinθ; then prove that (secθ − tanθ)^2 = (1/q)

$$\mathrm{if}\:{q}\:=\:\mathrm{1}−{sin}\theta;\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\left({sec}\theta\:−\:{tan}\theta\right)^{\mathrm{2}} \:=\:\frac{\mathrm{1}}{{q}} \\ $$

Question Number 159844 Answers: 0 Comments: 0

Question Number 159842 Answers: 2 Comments: 4

if p−5 = 2(√6) then prove that p(√p)−(1/(p(√p))) = 22(√2)

$$\mathrm{if}\:{p}−\mathrm{5}\:=\:\mathrm{2}\sqrt{\mathrm{6}}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${p}\sqrt{{p}}−\frac{\mathrm{1}}{{p}\sqrt{{p}}}\:=\:\mathrm{22}\sqrt{\mathrm{2}} \\ $$

Question Number 159839 Answers: 1 Comments: 0

q=2(√(2(√2)))

$${q}=\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}} \\ $$

Question Number 159837 Answers: 1 Comments: 0

lim_(x→−∞) (√(2021x^2 −6x)) +((1021x^3 −5x))^(1/3) =?

$$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt{\mathrm{2021}{x}^{\mathrm{2}} −\mathrm{6}{x}}\:+\sqrt[{\mathrm{3}}]{\mathrm{1021}{x}^{\mathrm{3}} −\mathrm{5}{x}}\:=? \\ $$

Question Number 159829 Answers: 0 Comments: 2

((y/b))^(2/3) +((x/a))^(2/3) =1 find the length of the line

$$\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} =\mathrm{1}\:\: \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}} \\ $$

Question Number 159828 Answers: 0 Comments: 6

Question Number 159817 Answers: 0 Comments: 0

Question Number 159823 Answers: 2 Comments: 0

Question Number 159796 Answers: 1 Comments: 0

Montrer que la suite de^ finie par u_n =Σ_(k=1) ^n (x^k /k) est une suite de Cauchy.

$$\mathrm{Montrer}\:\mathrm{que}\:\mathrm{la}\:\mathrm{suite}\:\mathrm{d}\acute {\mathrm{e}finie}\:\mathrm{par}\: \\ $$$${u}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{x}^{{k}} }{{k}}\:\mathrm{est}\:\mathrm{une}\:\mathrm{suite}\:\mathrm{de}\:\mathrm{Cauchy}. \\ $$

Question Number 159794 Answers: 1 Comments: 8

Question Number 159787 Answers: 0 Comments: 2

if cos^4 θ − sin^4 θ = 2 − 5cosθ then find the value of θ

$$\mathrm{if}\:{cos}^{\mathrm{4}} \theta\:−\:{sin}^{\mathrm{4}} \theta\:=\:\mathrm{2}\:−\:\mathrm{5}{cos}\theta \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\theta \\ $$

Question Number 159786 Answers: 0 Comments: 0

Work out and sketch P_y orbitals

$$\mathrm{Work}\:\mathrm{out}\:\mathrm{and}\:\mathrm{sketch}\:\mathrm{P}_{\mathrm{y}} \:\mathrm{orbitals} \\ $$

Question Number 159785 Answers: 0 Comments: 0

work out and sketch d−orbital for the function i) f_1 =3Cos^2 θ−1 i) f_2 =SinθCosθCosφ

$$\mathrm{work}\:\mathrm{out}\:\mathrm{and}\:\mathrm{sketch}\:\mathrm{d}−\mathrm{orbital}\:\mathrm{for}\:\mathrm{the}\:\mathrm{function} \\ $$$$\left.\mathrm{i}\right)\:\mathrm{f}_{\mathrm{1}} =\mathrm{3Cos}^{\mathrm{2}} \theta−\mathrm{1} \\ $$$$\left.\mathrm{i}\right)\:\mathrm{f}_{\mathrm{2}} =\mathrm{Sin}\theta\mathrm{Cos}\theta\mathrm{Cos}\phi \\ $$

Question Number 159784 Answers: 0 Comments: 1

Question Number 159939 Answers: 1 Comments: 2

U_(n+2) −2U_(n+1) +U_n =800

$$\mathrm{U}_{{n}+\mathrm{2}} −\mathrm{2U}_{{n}+\mathrm{1}} +\mathrm{U}_{{n}} =\mathrm{800} \\ $$

Question Number 159777 Answers: 2 Comments: 1

if x + y = (√7) and x^2 − y^2 = (√(35)) ; then find the value of 16xy(x^2 + y^2 )

$$\mathrm{if}\:{x}\:+\:{y}\:=\:\sqrt{\mathrm{7}}\:\mathrm{and}\:{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:=\:\sqrt{\mathrm{35}}\:; \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{16}{xy}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \right) \\ $$

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