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Question Number 29202 Answers: 1 Comments: 0

Find area between by y=1 and y=((1−x^2 )/(1+x^2 )) .

$${Find}\:{area}\:{between}\:{by}\:{y}=\mathrm{1}\:\:{and} \\ $$$${y}=\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:. \\ $$

Question Number 29201 Answers: 2 Comments: 0

Question Number 29198 Answers: 1 Comments: 1

Question Number 29196 Answers: 0 Comments: 0

Let s = n_c_1 − (1+(1/2))n_c_2 +(1+(1/2)+(1/3))n_c_3 +.......+(−1)^(n−1) (1+(1/2)+(1/3)+....+(1/n))n_c_n then prove that s×n =1.

$$\mathrm{Let}\:\mathrm{s}\:=\:\mathrm{n}_{\mathrm{c}_{\mathrm{1}} } \:−\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{2}} } \:+\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{3}} } \\ $$$$+.......+\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+....+\frac{\mathrm{1}}{\mathrm{n}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{n}} } \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{s}×\mathrm{n}\:=\mathrm{1}. \\ $$

Question Number 29231 Answers: 1 Comments: 0

Question Number 29180 Answers: 1 Comments: 0

lim_(x → a) ((((x)^(1/m) − (a)^(1/m) )/((x)^(1/n) − (a)^(1/n) ))) Don′t use L′hospital rules :-)

$$\underset{\mathrm{x}\:\rightarrow\:\mathrm{a}} {\mathrm{lim}}\:\left(\frac{\sqrt[{\mathrm{m}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{m}}]{\mathrm{a}}}{\sqrt[{\mathrm{n}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{n}}]{\mathrm{a}}}\right) \\ $$$$\left.\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{hospital}\:\mathrm{rules}\::-\right) \\ $$

Question Number 29173 Answers: 1 Comments: 0

find cos(5α) interms of cosα then find the value of cos((π/(10))).

$${find}\:{cos}\left(\mathrm{5}\alpha\right)\:{interms}\:{of}\:{cos}\alpha\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$${cos}\left(\frac{\pi}{\mathrm{10}}\right). \\ $$

Question Number 29172 Answers: 1 Comments: 0

Question Number 29171 Answers: 0 Comments: 0

Question Number 29170 Answers: 0 Comments: 0

Question Number 29169 Answers: 0 Comments: 1

factorize inside R[x] the polynomial p(x)= x^8 −1.

$${factorize}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynomial} \\ $$$${p}\left({x}\right)=\:{x}^{\mathrm{8}} −\mathrm{1}. \\ $$

Question Number 29168 Answers: 0 Comments: 1

Question Number 29167 Answers: 0 Comments: 1

let give S_n = Σ_(k=1) ^(n−1) sin(((kπ)/n)) find lim_(n→+∞) (S_n /n) .

$${let}\:{give}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} {sin}\left(\frac{{k}\pi}{{n}}\right)\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{S}_{{n}} }{{n}}\:\:. \\ $$

Question Number 29166 Answers: 0 Comments: 1

simlify S_n = Σ_(k=1) ^n k(1+i)^(k−1) .

$${simlify}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}\left(\mathrm{1}+{i}\right)^{{k}−\mathrm{1}} \:\:\:\:. \\ $$

Question Number 29165 Answers: 0 Comments: 1

give the factorization inside C[x] for p(x)= x^4 −((1−i(√3))/2) .

$${give}\:{the}\:{factorization}\:{inside}\:{C}\left[{x}\right]\:{for} \\ $$$${p}\left({x}\right)=\:\:{x}^{\mathrm{4}} \:−\frac{\mathrm{1}−{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\:. \\ $$

Question Number 29164 Answers: 0 Comments: 1

let put α= 1+i(√3) simlify A_n = Σ_(k=0) ^n α^k .

$${let}\:{put}\:\alpha=\:\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\:\:\:\:{simlify} \\ $$$${A}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\alpha^{{k}} \:\:\:. \\ $$

Question Number 29163 Answers: 0 Comments: 0

let give (n,p) from N^2 and 1≤p≤n prove that Σ_(k=0) ^p C_n ^k C_(n−k) ^(p−k) ==2^p C_n ^p .

$${let}\:{give}\:\left({n},{p}\right)\:{from}\:{N}^{\mathrm{2}} \:{and}\:\mathrm{1}\leqslant{p}\leqslant{n}\:{prove}\:{that}\: \\ $$$$\sum_{{k}=\mathrm{0}} ^{{p}} \:{C}_{{n}} ^{{k}} \:{C}_{{n}−{k}} ^{{p}−{k}} ==\mathrm{2}^{{p}} \:\:{C}_{{n}} ^{{p}} . \\ $$$$ \\ $$

Question Number 29162 Answers: 0 Comments: 1

find find I= ∫_1 ^3 ((∣x−2∣)/((x^2 −4x)^2 ))dx .

$${find}\:\:{find}\:{I}=\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\:\frac{\mid{x}−\mathrm{2}\mid}{\left({x}^{\mathrm{2}} −\mathrm{4}{x}\right)^{\mathrm{2}} }{dx}\:. \\ $$

Question Number 29161 Answers: 1 Comments: 1

let give f(x)=(√(x−1+2(√(x−2)))) +(√(x−1−2(√(x−2)))) 1) simlify f(x) 2) solve inside N^2 the equation f(x)=y.

$${let}\:{give}\:{f}\left({x}\right)=\sqrt{{x}−\mathrm{1}+\mathrm{2}\sqrt{{x}−\mathrm{2}}}\:\:+\sqrt{{x}−\mathrm{1}−\mathrm{2}\sqrt{{x}−\mathrm{2}}} \\ $$$$\left.\mathrm{1}\right)\:{simlify}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{solve}\:{inside}\:\mathbb{N}^{\mathrm{2}} \:{the}\:{equation}\:{f}\left({x}\right)={y}. \\ $$

Question Number 29149 Answers: 1 Comments: 0

(u_n )_n is arithmetic progression/ u_n = u_0 +nr find S_n = Σ_(k=0) ^n u_k ^2 .

$$\left({u}_{{n}} \right)_{{n}} \:\:{is}\:{arithmetic}\:{progression}/\:{u}_{{n}} =\:{u}_{\mathrm{0}} +{nr}\: \\ $$$${find}\:{S}_{{n}} =\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:{u}_{{k}} ^{\mathrm{2}} .\: \\ $$

Question Number 29148 Answers: 0 Comments: 1

let give the sequence (u_n ) /u_0 =1 and u_1 =2 and ∀ n ∈N 2u_(n+2) =3 u_(n+1) −u_n . let give the sequence (v_n ) / v_n = u_(n+1) −u_n . 1) prove that (v_n ) is geometric .find v_n in terms of n 2) find u_n in terms of n.

$${let}\:{give}\:{the}\:{sequence}\:\left({u}_{{n}} \right)\:/{u}_{\mathrm{0}} =\mathrm{1}\:{and}\:{u}_{\mathrm{1}} =\mathrm{2}\:{and} \\ $$$$\forall\:{n}\:\in{N}\:\:\:\mathrm{2}{u}_{{n}+\mathrm{2}} =\mathrm{3}\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} .\:{let}\:{give}\:{the}\:{sequence}\:\left({v}_{{n}} \right)\:/ \\ $$$${v}_{{n}} =\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} \:. \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\left({v}_{{n}} \right)\:{is}\:{geometric}\:.{find}\:{v}_{{n}} {in}\:{terms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$

Question Number 29140 Answers: 0 Comments: 6

Find no. of rational roots of f(x)= 2x^(98) +3x^(97) +2x^(96) +.....+2x+3=0.

$${Find}\:{no}.\:{of}\:{rational}\:{roots}\:{of}\:{f}\left({x}\right)= \\ $$$$\mathrm{2}{x}^{\mathrm{98}} +\mathrm{3}{x}^{\mathrm{97}} +\mathrm{2}{x}^{\mathrm{96}} +.....+\mathrm{2}{x}+\mathrm{3}=\mathrm{0}. \\ $$

Question Number 29138 Answers: 0 Comments: 4

Find number of polynomials p(x) with intgral coefficients such that p(1)=2, p(3)=1

$${Find}\:{number}\:{of}\:{polynomials}\:{p}\left({x}\right) \\ $$$${with}\:{intgral}\:{coefficients}\:{such}\:{that} \\ $$$${p}\left(\mathrm{1}\right)=\mathrm{2},\:{p}\left(\mathrm{3}\right)=\mathrm{1} \\ $$

Question Number 29134 Answers: 0 Comments: 3

Question Number 29131 Answers: 1 Comments: 2

If tan^2 atan^2 b+tan^2 btan^2 c+tan^2 ctan^2 a +2tan^2 atan^2 btan^2 c=1 then find the value of: sin^2 a+sin^2 b+sin^2 c

$${If}\:\mathrm{tan}^{\mathrm{2}} {a}\mathrm{tan}\:^{\mathrm{2}} {b}+\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}+\mathrm{tan}^{\mathrm{2}} {c}\mathrm{tan}\:^{\mathrm{2}} {a} \\ $$$$+\mathrm{2tan}^{\mathrm{2}} {a}\mathrm{tan}^{\mathrm{2}} {b}\mathrm{tan}\:^{\mathrm{2}} {c}=\mathrm{1} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}: \\ $$$$\mathrm{sin}\:^{\mathrm{2}} {a}+\mathrm{sin}\:^{\mathrm{2}} {b}+\mathrm{sin}\:^{\mathrm{2}} {c} \\ $$

Question Number 29136 Answers: 0 Comments: 1

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