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Question Number 223801 Answers: 0 Comments: 1

sorry i mean p_h ∈P (prime set) lim_(h→∞) (p_(h+1) /p_h )=??

$$\mathrm{sorry}\:\:\mathrm{i}\:\mathrm{mean}\:{p}_{{h}} \in\mathbb{P}\:\left(\mathrm{prime}\:\mathrm{set}\right) \\ $$$$\underset{{h}\rightarrow\infty} {\mathrm{lim}}\:\frac{{p}_{{h}+\mathrm{1}} }{{p}_{{h}} }=?? \\ $$

Question Number 223800 Answers: 1 Comments: 0

Given f(x)= ((x^2 +14x+40)/(g(x)))−43 h(x)= ((g(x)+51)/(x+4)) m(x)= ((h(x)−9)/(x−2)) , x≠2 m(2)= 2043. If f(x) divided by x^2 +8x−20 gives remainder is M(x)=ax+b then the value of M(98)=?

Question Number 223786 Answers: 0 Comments: 4

Evaluate ; ∫ (√( tan x)) dx , Using feynman′s trick

$$ \\ $$$$\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:;\:\int\:\sqrt{\:\boldsymbol{\mathrm{tan}}\:\boldsymbol{{x}}}\:\boldsymbol{\mathrm{d}{x}}\:,\:\boldsymbol{\mathrm{Using}}\:\boldsymbol{\mathrm{feynman}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{trick}} \\ $$$$ \\ $$

Question Number 223783 Answers: 2 Comments: 1

Question Number 223779 Answers: 1 Comments: 0

Question Number 223778 Answers: 1 Comments: 0

lim_(N→∞) (p_(N+1) /p_N )=??? , p_1 =2 , p_2 =3 ,p_3 =5 ....

$$\underset{{N}\rightarrow\infty} {\mathrm{lim}}\:\frac{{p}_{{N}+\mathrm{1}} }{{p}_{{N}} }=???\:\:,\:{p}_{\mathrm{1}} =\mathrm{2}\:,\:{p}_{\mathrm{2}} =\mathrm{3}\:,{p}_{\mathrm{3}} =\mathrm{5}\:.... \\ $$

Question Number 223741 Answers: 2 Comments: 1

Question Number 223735 Answers: 0 Comments: 0

for all n ∈ Z , Show that τ ( ϕ ( n )) ≥ ϕ (τ (n ))

$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\:{n}\:\in\:\mathbb{Z}\:, \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}\:\tau\:\left(\:\varphi\:\left(\:{n}\:\right)\right)\:\geqslant\:\varphi\:\left(\tau\:\left({n}\:\right)\right) \\ $$$$ \\ $$

Question Number 223734 Answers: 1 Comments: 0

Question Number 223728 Answers: 1 Comments: 0

∫_0_ ^1 ((ln(1+(√x))∙ln(1+x))/(1+(√x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}_{\:} } ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\sqrt{{x}}\right)\centerdot\mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+\sqrt{{x}}}\:\mathrm{d}{x} \\ $$

Question Number 223724 Answers: 2 Comments: 0

A rubber ball of mass m radius R and densityρ is released from a depth h under a fluid of density σ(σ>ρ) i) How high will the ball bounce on the the fluid ?Ignore any obstacles ii)time taken by the ball to reach the surface iii)time in air

$$\: \\ $$$$\mathrm{A}\:\mathrm{rubber}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\: \\ $$$$\mathrm{radius}\:\mathrm{R}\:\mathrm{and}\:\mathrm{density}\rho\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{depth}\:\mathrm{h}\:\mathrm{under}\:\mathrm{a}\:\mathrm{fluid}\:\mathrm{of}\:\mathrm{density}\:\sigma\left(\sigma>\rho\right) \\ $$$$\left.\mathrm{i}\right) \\ $$$$\:\mathrm{How}\:\mathrm{high}\:\mathrm{will}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{bounce}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{the}\:\mathrm{fluid}\:?\mathrm{Ignore}\:\mathrm{any} \\ $$$$\mathrm{obstacles} \\ $$$$\left.\mathrm{ii}\right)\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{the}\: \\ $$$$\mathrm{surface} \\ $$$$\left.\mathrm{iii}\right)\mathrm{time}\:\mathrm{in}\:\mathrm{air} \\ $$

Question Number 223720 Answers: 1 Comments: 1

One end of a string is attached to a solid wall and the other end is hanging from a smooth pulley 2 m away fromthe wall. A point mass M of mass 2 kg is attached to the string 1 m away from the wall and an object m of mass 0.5 kg is attached to the hanging end of the string. The object is fixed in such a way that the part of the string inside the wall and pully is horizontal and the rest is vertical. If mass m is released, with what speed will mass M hit the wall?

$$ \\ $$$$\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{string}\:\mathrm{is} \\ $$$$\mathrm{attached}\:\mathrm{to}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{smooth}\:\mathrm{pulley}\:\mathrm{2}\:\mathrm{m}\:\mathrm{away}\: \\ $$$$\mathrm{fromthe}\:\mathrm{wall}.\:\mathrm{A}\:\mathrm{point}\:\mathrm{mass}\: \\ $$$$\mathrm{M}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{string}\:\mathrm{1}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{wall}\:\mathrm{and}\:\mathrm{an}\:\mathrm{object}\:\mathrm{m}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{0}.\mathrm{5}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{hanging}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{string}.\: \\ $$$$\mathrm{The}\:\mathrm{object}\:\mathrm{is}\:\mathrm{fixed}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a} \\ $$$$\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{string}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{and} \\ $$$$\mathrm{pully}\:\mathrm{is}\:\mathrm{horizontal}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{rest}\:\mathrm{is}\:\mathrm{vertical}.\:\mathrm{If}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{is} \\ $$$$\mathrm{released},\:\mathrm{with}\:\mathrm{what}\:\mathrm{speed}\:\mathrm{will} \\ $$$$\mathrm{mass}\:\mathrm{M}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{wall}? \\ $$

Question Number 223712 Answers: 3 Comments: 1