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Question Number 184792    Answers: 1   Comments: 2

Evaluate lim_(x→0) ((tan x−sin x)/(sin^3 x))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}−\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}} \\ $$$$ \\ $$

Question Number 184791    Answers: 0   Comments: 2

Evaluate lim_(x→0) ((e^x +e^(−x) −2)/x^2 )

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{e}^{{x}} +{e}^{−{x}} −\mathrm{2}}{{x}^{\mathrm{2}} } \\ $$

Question Number 184790    Answers: 2   Comments: 2

Evaluate lim_(x→0) (((1+x)^6 −1)/((1+x)^5 −1))

$${Evaluate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{6}} −\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{5}} −\mathrm{1}} \\ $$

Question Number 184787    Answers: 0   Comments: 2

x^4 +16x^3 +9x^2 +256x+256=0 Find the values of x?

$$\mathrm{x}^{\mathrm{4}} +\mathrm{16x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{256x}+\mathrm{256}=\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}? \\ $$

Question Number 184775    Answers: 1   Comments: 2

(1/(6 + (9/(6 + ((25)/(6 + ((49)/(6 + ((81)/(6+ ......)) )) )) )) )) =?

$$\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{6}\:+\:\frac{\mathrm{9}}{\mathrm{6}\:+\:\:\frac{\mathrm{25}}{\mathrm{6}\:\:+\:\:\frac{\mathrm{49}}{\mathrm{6}\:+\:\frac{\mathrm{81}}{\mathrm{6}+\:......}\:\:\:\:\:}\:\:\:\:\:}\:\:}\:\:\:\:\:\:\:\:}\:\:=? \\ $$$$ \\ $$$$ \\ $$

Question Number 184774    Answers: 1   Comments: 2

Calcul the sum 1.Σx(1+x^2 )^(1/2) 2.Σxarctan(x) 3.Σe^x sinx 4.Σ(2x+1)^(20) 5.Σ(√(a^2 −x^2 )) a>0 6.Σxsinx

$${Calcul}\:{the}\:{sum} \\ $$$$\mathrm{1}.\Sigma{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\mathrm{2}.\Sigma{xarctan}\left({x}\right) \\ $$$$\mathrm{3}.\Sigma{e}^{{x}} {sinx} \\ $$$$\mathrm{4}.\Sigma\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{20}} \\ $$$$\mathrm{5}.\Sigma\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} \:}\:{a}>\mathrm{0} \\ $$$$\mathrm{6}.\Sigma{xsinx} \\ $$

Question Number 184773    Answers: 2   Comments: 1

lim_(x→1) ((ax+b)/( (√(1+3x))−2))=c 2a−2b+3c=? (a,b,c)≠0 pease solution????

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}}{\:\sqrt{\mathrm{1}+\mathrm{3x}}−\mathrm{2}}=\mathrm{c} \\ $$$$\mathrm{2a}−\mathrm{2b}+\mathrm{3c}=? \\ $$$$\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)\neq\mathrm{0} \\ $$$$\mathrm{pease}\:\mathrm{solution}???? \\ $$

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

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