Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1825

Question Number 26722    Answers: 0   Comments: 0

lim_(x→−1^+ ) (1+x+x^2 +x^3 +...up to ∞)=? lim_(x→−1^− ) (1+x+x^2 +x^3 +...up to ∞)=?

$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +...\mathrm{up}\:\mathrm{to}\:\infty\right)=? \\ $$$$\underset{{x}\rightarrow−\mathrm{1}^{−} } {\mathrm{lim}}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +...\mathrm{up}\:\mathrm{to}\:\infty\right)=? \\ $$

Question Number 26721    Answers: 0   Comments: 1

−2y(y−12)(y−1)or(y−12)(−2y^2 −2y) both are same.

$$−\mathrm{2}{y}\left({y}−\mathrm{12}\right)\left({y}−\mathrm{1}\right){or}\left({y}−\mathrm{12}\right)\left(−\mathrm{2}{y}^{\mathrm{2}} −\mathrm{2}{y}\right)\:\:{both}\:{are}\:{same}. \\ $$

Question Number 26713    Answers: 0   Comments: 0

2sin (3x)<1

$$\mathrm{2sin}\:\left(\mathrm{3}{x}\right)<\mathrm{1} \\ $$

Question Number 26712    Answers: 1   Comments: 0

If ∣x∣ < 1, then the coefficient of x^n in the expansion of (1+x+x^2 +x^3 +x^4 +...)^2 is

$$\mathrm{If}\:\:\mid{x}\mid\:<\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{{n}} \:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +{x}^{\mathrm{4}} +...\right)^{\mathrm{2}} \:\mathrm{is} \\ $$

Question Number 26711    Answers: 0   Comments: 1

ABC is a right tringle.prove it?

$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{tringle}.\mathrm{prove}\:\mathrm{it}? \\ $$

Question Number 26703    Answers: 0   Comments: 0

The total number of dissimilar terms in the expansion of (x_1 +x_2 +...+x_n )^3 is

$$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{dissimilar}\:\mathrm{terms}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} +...+{x}_{{n}} \right)^{\mathrm{3}} \:\mathrm{is} \\ $$

Question Number 26694    Answers: 1   Comments: 0

divide x^6 −y^6 by the product of x^2 +x^ y+y^(2 ) and x−y.

$${divide}\:{x}^{\mathrm{6}} −{y}^{\mathrm{6}} \:{by}\:{the}\:{product}\:{of}\:{x}^{\mathrm{2}} +{x}^{} {y}+{y}^{\mathrm{2}\:} \:{and}\:{x}−{y}. \\ $$

Question Number 26693    Answers: 0   Comments: 3

STATEMENT-1: The angle between one of the lines represented by ax^2 + 2hxy + by^2 = 0 and one of the lines represented by (a + 2008)x^2 + 2hxy + (b + 2008)y^2 = 0 is equal to angle between other two lines of the system. and STATEMENT-2: The pair of lines given by a^2 x^2 + 2008(a + b)xy + b^2 y^2 = 0 is equally inclined to the pair given by ax^2 + 2008xy + by^2 = 0.

$${STATEMENT}-\mathrm{1}:\:{The}\:{angle}\:{between} \\ $$$${one}\:{of}\:{the}\:{lines}\:{represented}\:{by}\:{ax}^{\mathrm{2}} \:+ \\ $$$$\mathrm{2}{hxy}\:+\:{by}^{\mathrm{2}} \:=\:\mathrm{0}\:{and}\:{one}\:{of}\:{the}\:{lines} \\ $$$${represented}\:{by}\:\left({a}\:+\:\mathrm{2008}\right){x}^{\mathrm{2}} \:+\:\mathrm{2}{hxy} \\ $$$$+\:\left({b}\:+\:\mathrm{2008}\right){y}^{\mathrm{2}} \:=\:\mathrm{0}\:{is}\:{equal}\:{to}\:{angle} \\ $$$${between}\:{other}\:{two}\:{lines}\:{of}\:{the} \\ $$$${system}. \\ $$$$\boldsymbol{{and}} \\ $$$${STATEMENT}-\mathrm{2}:\:{The}\:{pair}\:{of}\:{lines} \\ $$$${given}\:{by}\:{a}^{\mathrm{2}} {x}^{\mathrm{2}} \:+\:\mathrm{2008}\left({a}\:+\:{b}\right){xy}\:+\:{b}^{\mathrm{2}} {y}^{\mathrm{2}} \\ $$$$=\:\mathrm{0}\:{is}\:{equally}\:{inclined}\:{to}\:{the}\:{pair} \\ $$$${given}\:{by}\:{ax}^{\mathrm{2}} \:+\:\mathrm{2008}{xy}\:+\:{by}^{\mathrm{2}} \:=\:\mathrm{0}. \\ $$

Question Number 26686    Answers: 1   Comments: 1

Question Number 26681    Answers: 0   Comments: 1

f:R×R→R such that f(x+iy)=(√(x^2 +y^2 .)) Then f is a) many−one and into function b) one−one and onto function c) many−one and onto function d) one−one and into function

$${f}:{R}×{R}\rightarrow{R}\:{such}\:{that}\:{f}\left({x}+{iy}\right)=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} .} \\ $$$${Then}\:{f}\:{is} \\ $$$$\left.{a}\right)\:{many}−{one}\:{and}\:{into}\:{function} \\ $$$$\left.{b}\right)\:{one}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{c}\right)\:{many}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{d}\right)\:{one}−{one}\:{and}\:{into}\:{function} \\ $$

Question Number 26680    Answers: 1   Comments: 0

(b−c)x^2 +(c−a)x+(a−b)=0 if the eqation roots are eqal you proved that 2b=a+c.

$$\left({b}−{c}\right){x}^{\mathrm{2}} +\left({c}−{a}\right){x}+\left({a}−{b}\right)=\mathrm{0}\:{if}\:{the}\: \\ $$$${eqation}\:{roots}\:\:{are}\:{eqal}\:{you}\:{proved}\:{that} \\ $$$$\mathrm{2}{b}={a}+{c}. \\ $$

Question Number 26652    Answers: 0   Comments: 2

Question Number 26649    Answers: 1   Comments: 1

Solve the equation:x+y=5−−−i x^x + y^y =31−−−ii No trial and error

$${Solve}\:{the}\:{equation}:{x}+{y}=\mathrm{5}−−−{i} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{{x}} +\:{y}^{{y}} =\mathrm{31}−−−{ii} \\ $$$${No}\:{trial}\:{and}\:{error} \\ $$$$ \\ $$

Question Number 26644    Answers: 1   Comments: 0

Question Number 26642    Answers: 2   Comments: 0

9x^2 +41x−204=0. solved it.

$$\mathrm{9}{x}^{\mathrm{2}} +\mathrm{41}{x}−\mathrm{204}=\mathrm{0}.\:{solved}\:{it}. \\ $$

Question Number 26638    Answers: 1   Comments: 0

x^3 −8x^2 +7 factorise it.

$$\mathrm{x}^{\mathrm{3}} −\mathrm{8x}^{\mathrm{2}} +\mathrm{7}\:\:\mathrm{factorise}\:\mathrm{it}. \\ $$

Question Number 26634    Answers: 1   Comments: 1

Question Number 26633    Answers: 0   Comments: 0

find the consumption function when MPC is c′(y)=0.8+0.1(√(y )) and that C=Y when Y=100

$$\mathrm{find}\:\mathrm{the}\:\mathrm{consumption}\:\mathrm{function}\:\mathrm{when}\:\mathrm{MPC}\:\mathrm{is}\:\mathrm{c}'\left(\mathrm{y}\right)=\mathrm{0}.\mathrm{8}+\mathrm{0}.\mathrm{1}\sqrt{\mathrm{y}\:} \\ $$$$\mathrm{and}\:\mathrm{that}\:\mathrm{C}=\mathrm{Y}\:\mathrm{when}\:\mathrm{Y}=\mathrm{100} \\ $$

Question Number 26631    Answers: 0   Comments: 1

∫_0 ^∞ (1/x^2 )dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$$$ \\ $$

Question Number 26626    Answers: 1   Comments: 0

Question Number 26625    Answers: 1   Comments: 0

3y−2x+7=0 x^2 −4y^2 −21=0

$$\mathrm{3y}−\mathrm{2x}+\mathrm{7}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} −\mathrm{21}=\mathrm{0} \\ $$

Question Number 26623    Answers: 2   Comments: 0

distance between 2 places A and B on road is 70 km. a car starts from A and other from B .if they travel in same direction they will meet after 7 hours. if they travel towards each other they will meet after 1 hour then find their speeds

$$\mathrm{distance}\:\mathrm{between}\:\mathrm{2}\:\mathrm{places}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{on} \\ $$$$\mathrm{road}\:\mathrm{is}\:\mathrm{70}\:\mathrm{km}.\:\mathrm{a}\:\mathrm{car}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{A}\:\mathrm{and}\:\mathrm{other}\: \\ $$$$\mathrm{from}\:\mathrm{B}\:.\mathrm{if}\:\mathrm{they}\:\mathrm{travel}\:\mathrm{in}\:\mathrm{same}\:\mathrm{direction} \\ $$$$\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{7}\:\mathrm{hours}.\:\mathrm{if}\:\mathrm{they}\:\mathrm{travel} \\ $$$$\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after} \\ $$$$\mathrm{1}\:\mathrm{hour}\:\mathrm{then}\:\mathrm{find}\:\mathrm{their}\:\mathrm{speeds} \\ $$

Question Number 26591    Answers: 1   Comments: 1

Prove lim_(x→−1) (1+x)ln (1+x)=0

$$\mathrm{Prove} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\left(\mathrm{1}+{x}\right)\mathrm{ln}\:\left(\mathrm{1}+{x}\right)=\mathrm{0} \\ $$

Question Number 26583    Answers: 0   Comments: 2

find the decomposition in C[x] then R[x] for the rationsl fraction F(x)= ((1 )/(x^(2n) −1)) .with n integer not 0

$${find}\:{the}\:{decomposition}\:{in}\:\mathbb{C}\left[{x}\right]\:{then}\:\mathbb{R}\left[{x}\right] \\ $$$${for}\:{the}\:{rationsl}\:{fraction} \\ $$$${F}\left({x}\right)=\:\:\frac{\mathrm{1}\:}{{x}^{\mathrm{2}{n}} −\mathrm{1}}\:\:.{with}\:{n}\:{integer}\:{not}\:\mathrm{0} \\ $$

Question Number 26582    Answers: 0   Comments: 1

p is a polynomial having the roots x_1 ,x_2 ,...x_n with x_i ≠ x_j fori≠j give the decomposition of the fravtion F(x)= ((p^′ (x))/(p(x)))

$${p}\:{is}\:{a}\:{polynomial}\:{having}\:{the}\:{roots}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,...{x}_{{n}} \\ $$$${with}\:{x}_{{i}} \neq\:{x}_{{j}} \:{fori}\neq{j}\:{give}\:{the}\:{decomposition} \\ $$$${of}\:{the}\:{fravtion}\:{F}\left({x}\right)=\:\frac{{p}^{'} \left({x}\right)}{{p}\left({x}\right)} \\ $$

Question Number 26581    Answers: 0   Comments: 0

  Pg 1820      Pg 1821      Pg 1822      Pg 1823      Pg 1824      Pg 1825      Pg 1826      Pg 1827      Pg 1828      Pg 1829   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com