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Question Number 184769 Answers: 0 Comments: 2

Question Number 184768 Answers: 1 Comments: 1

Σ_(n=o) ^(+oo) (x^n /(4n^2 −1))

$$\underset{{n}={o}} {\overset{+{oo}} {\sum}}\:\frac{{x}^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 184757 Answers: 2 Comments: 2

Which function has a crisis point? a)y=x^3 +2x+6 b)y=(x)^(1/4) c)y=((15)/x) d)y=e^x e)y=(x)^(1/3)

$$\mathrm{Which}\:\mathrm{function}\:\mathrm{has}\:\mathrm{a}\:\mathrm{crisis}\:\mathrm{point}? \\ $$$$\left.\mathrm{a}\right)\mathrm{y}=\mathrm{x}^{\mathrm{3}} +\mathrm{2x}+\mathrm{6} \\ $$$$\left.\mathrm{b}\right)\mathrm{y}=\sqrt[{\mathrm{4}}]{\mathrm{x}} \\ $$$$\left.\mathrm{c}\right)\mathrm{y}=\frac{\mathrm{15}}{\mathrm{x}} \\ $$$$\left.\mathrm{d}\right)\mathrm{y}=\mathrm{e}^{\boldsymbol{\mathrm{x}}} \\ $$$$\left.\mathrm{e}\right)\mathrm{y}=\sqrt[{\mathrm{3}}]{\mathrm{x}} \\ $$

Question Number 184753 Answers: 1 Comments: 0

Question Number 184744 Answers: 1 Comments: 1

given that the 5th term of an AP is more than its firs term by 12. and the 6th term is more than the first term by 10. find the fist term? common difference and 100th term

$${given}\:{that}\:{the}\:\mathrm{5}{th}\:{term}\:{of}\:{an}\:{AP}\:{is}\:{more}\:{than}\:{its}\:{firs}\:{term}\:{by}\:\mathrm{12}.\:{and}\:{the}\:\mathrm{6}{th}\:{term}\:{is}\:{more}\:{than}\:{the}\:{first}\:{term}\:{by}\:\mathrm{10}.\:{find}\:{the}\:{fist}\:{term}?\:{common}\:{difference}\:{and}\:\mathrm{100}{th}\:{term} \\ $$$$ \\ $$

Question Number 184739 Answers: 1 Comments: 1

Number of linear functions be defined f:[−1, 1]→[0,2] is a)1 b)2 c)3 d)4

$${Number}\:{of}\:{linear}\:{functions}\: \\ $$$${be}\:{defined}\:{f}:\left[−\mathrm{1},\:\mathrm{1}\right]\rightarrow\left[\mathrm{0},\mathrm{2}\right]\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:{c}\right)\mathrm{3}\:\:\:{d}\right)\mathrm{4} \\ $$

Question Number 184738 Answers: 1 Comments: 0

α , β are roots of , x^( 2) −x−1=0 ( α > β ) and , t_( n) = ((α^( n) − β^( n) )/(α−β)) ( n ∈ N ), if , b_1 =1 , b_( n) = t_( n−1) +t_( n−2) ( n ≥2 ) find the value of S = Σ_(n=1) ^∞ (( b_( n) )/(10^( n) )) =?

$$ \\ $$$$\alpha\:\:,\:\beta\:\:{are}\:{roots}\:{of}\:\:,\:{x}^{\:\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left(\:\:\alpha\:>\:\beta\:\right)\:{and}\:,\:\:{t}_{\:{n}} =\:\frac{\alpha^{\:{n}} −\:\beta^{\:{n}} }{\alpha−\beta} \\ $$$$\:\left(\:{n}\:\in\:\mathbb{N}\:\right),\:{if}\:,\:{b}_{\mathrm{1}} =\mathrm{1}\:,\:{b}_{\:{n}} =\:{t}_{\:{n}−\mathrm{1}} +{t}_{\:{n}−\mathrm{2}} \\ $$$$\:\:\:\left(\:{n}\:\geqslant\mathrm{2}\:\right)\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{b}_{\:{n}} }{\mathrm{10}^{\:{n}} }\:=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 184735 Answers: 0 Comments: 3

f(x,y)=((√(3xy^2 )))(((x^5 y^2 ))^(1/5) ) f^′ (x,y)=? f′′(x,y)=?

$$ \\ $$$${f}\left({x},{y}\right)=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${f}^{'} \left({x},{y}\right)=?\:\:\:\:\:{f}''\left({x},{y}\right)=? \\ $$$$ \\ $$

Question Number 184731 Answers: 1 Comments: 0

Express this function in both its Cartesian and polar form f(z) = ze^(iz) . Help!

$$\mathrm{Express}\:\mathrm{this}\:\mathrm{function}\:\mathrm{in}\:\mathrm{both}\:\mathrm{its} \\ $$$$\mathrm{Cartesian}\:\mathrm{and}\:\mathrm{polar}\:\mathrm{form} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)\:=\:\mathrm{ze}^{\mathrm{iz}} . \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184728 Answers: 5 Comments: 0

x^( 2) − 3x +1=0 α , β are roots : ( α^( 3) +(1/β) )^( 3) + ( β^^( 3) +(1/α) )^( 3) = ?

$$ \\ $$$$\:\:\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{3}{x}\:+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\alpha\:,\:\beta\:{are}\:{roots}\:: \\ $$$$\:\:\:\left(\:\alpha^{\:\mathrm{3}} \:+\frac{\mathrm{1}}{\beta}\:\right)^{\:\mathrm{3}} \:+\:\left(\:\beta^{\:^{\:\mathrm{3}} } \:+\frac{\mathrm{1}}{\alpha}\:\right)^{\:\mathrm{3}} =\:? \\ $$$$ \\ $$

Question Number 184726 Answers: 1 Comments: 0

Question Number 184724 Answers: 0 Comments: 1

Question Number 184720 Answers: 1 Comments: 0

y=((√(3xy^2 )))(((x^5 y^2 ))^(1/5) ) y′=? y^(′′) =?

$$ \\ $$$${y}=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${y}'=?\:\:\:\:\:\:{y}^{''} =? \\ $$

Question Number 184719 Answers: 1 Comments: 0

Question Number 184718 Answers: 2 Comments: 0

Question Number 184706 Answers: 1 Comments: 0

deg[3p(x)+Q(x)]=6 deg[p(x)+x^4 ]=5 deg[(((x^4 +1)p(x^2 ))/(x^3 ∙Q(x)))]=? deg=degree

$$\mathrm{deg}\left[\mathrm{3p}\left(\mathrm{x}\right)+\mathrm{Q}\left(\mathrm{x}\right)\right]=\mathrm{6} \\ $$$$\mathrm{deg}\left[\mathrm{p}\left(\mathrm{x}\right)+\mathrm{x}^{\mathrm{4}} \right]=\mathrm{5} \\ $$$$\mathrm{deg}\left[\frac{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)\mathrm{p}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \centerdot\mathrm{Q}\left(\mathrm{x}\right)}\right]=? \\ $$$$\mathrm{deg}=\mathrm{degree}\: \\ $$

Question Number 184705 Answers: 0 Comments: 0

Question Number 184683 Answers: 1 Comments: 0

x′′ − (5/t) x′ + (8/t^2 ) x = ((2 ln t)/t^2 ) solve the differential eqn

$${x}''\:−\:\frac{\mathrm{5}}{{t}}\:{x}'\:+\:\frac{\mathrm{8}}{{t}^{\mathrm{2}} }\:{x}\:=\:\frac{\mathrm{2}\:{ln}\:{t}}{{t}^{\mathrm{2}} } \\ $$$${solve}\:{the}\:{differential}\:{eqn} \\ $$

Question Number 184669 Answers: 0 Comments: 3

Question Number 184668 Answers: 0 Comments: 0

Question Number 184656 Answers: 1 Comments: 0

prove that the area of a triangle whose two sides are A^− and B^− is given by (1/2)∣A×B∣. Also find the direction−cosine of normal to this area. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{are}\:\overset{−} {\mathrm{A}}\:\mathrm{and}\:\overset{−} {\mathrm{B}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{A}×\mathrm{B}\mid. \\ $$$$\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{direction}−\mathrm{cosine} \\ $$$$\mathrm{of}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{this}\:\mathrm{area}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184655 Answers: 1 Comments: 0

prove that an angle inscribe in a semi−circle is a right angle. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{inscribe}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{semi}−\mathrm{circle}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184645 Answers: 1 Comments: 0

Question Number 184633 Answers: 1 Comments: 0

Question Number 184638 Answers: 0 Comments: 6

Question Number 184618 Answers: 1 Comments: 0

If xy≤ax^2 +2y^2 is always true for any 1≤x≤2, 2≤y≤3 Then find the range of a.

$$\mathrm{If}\:{xy}\leqslant{ax}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{always}\:\mathrm{true}\:\mathrm{for}\:\mathrm{any}\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2},\:\mathrm{2}\leqslant{y}\leqslant\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}. \\ $$

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