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Question Number 7887 Answers: 1 Comments: 0

Find the first four terms of the power series expansion of ((sinx)/(1 − x))

$${Find}\:{the}\:{first}\:{four}\:{terms}\:{of}\:{the}\:{power}\:{series}\: \\ $$$${expansion}\:{of}\:\:\:\:\:\frac{{sinx}}{\mathrm{1}\:−\:{x}}\:\:\: \\ $$

Question Number 7702 Answers: 0 Comments: 1

Question Number 7701 Answers: 0 Comments: 1

(x−2y

$$\left({x}−\mathrm{2}{y}\right. \\ $$$$ \\ $$

Question Number 7667 Answers: 1 Comments: 0

lim_(x→α) [x−x^2 log (1+(1/x))]

$$\underset{{x}\rightarrow\alpha} {\mathrm{lim}}\left[{x}−{x}^{\mathrm{2}} \mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\right] \\ $$

Question Number 7665 Answers: 1 Comments: 0

(d/dx)(√(x^2 −4))

$$\frac{{d}}{{dx}}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$

Question Number 7655 Answers: 2 Comments: 1

((8/x))^x = x^2 Show that x = 4

$$\left(\frac{\mathrm{8}}{{x}}\right)^{{x}} \:=\:\:{x}^{\mathrm{2}} \\ $$$$ \\ $$$${Show}\:{that}\:\:{x}\:=\:\mathrm{4} \\ $$

Question Number 7600 Answers: 1 Comments: 0

solve ∣((x^2 −3x−1)/(x^2 +x+1))∣<3 give solution

$${solve}\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\mid<\mathrm{3}\:\:{give}\:{solution} \\ $$

Question Number 7608 Answers: 1 Comments: 3

If x = cosΘ − sinΘ and y = cos2Θ Show that, y = x(√(2 − x^2 ))

$${If}\:\:{x}\:=\:{cos}\Theta\:−\:{sin}\Theta \\ $$$${and}\:\:{y}\:=\:{cos}\mathrm{2}\Theta \\ $$$${Show}\:{that},\:\: \\ $$$${y}\:=\:{x}\sqrt{\mathrm{2}\:−\:{x}^{\mathrm{2}} } \\ $$

Question Number 7544 Answers: 0 Comments: 7

Question Number 7326 Answers: 0 Comments: 2

Is it correct? floor(x)=⌊x⌋=[x] floor(x)={n ∣ n∈Z , x−1<n≤x} e.g.... floor(3)=3 floor(3.4)=3 floor(−2.5)=−3 floor(−π)=−4

$${Is}\:{it}\:{correct}? \\ $$$$\:\:{floor}\left({x}\right)=\lfloor{x}\rfloor=\left[{x}\right] \\ $$$$ \\ $$$$ \\ $$$${floor}\left({x}\right)=\left\{{n}\:\mid\:{n}\in\mathbb{Z}\:,\:{x}−\mathrm{1}<{n}\leqslant{x}\right\} \\ $$$${e}.{g}.... \\ $$$${floor}\left(\mathrm{3}\right)=\mathrm{3} \\ $$$${floor}\left(\mathrm{3}.\mathrm{4}\right)=\mathrm{3} \\ $$$${floor}\left(−\mathrm{2}.\mathrm{5}\right)=−\mathrm{3} \\ $$$${floor}\left(−\pi\right)=−\mathrm{4} \\ $$

Question Number 7314 Answers: 1 Comments: 1

Question Number 7316 Answers: 0 Comments: 1

x−y and y−x x={−2,−1,0,2,5} y={0,5,7,8,10}

$${x}−{y}\:{and}\:{y}−{x}\: \\ $$$${x}=\left\{−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{2},\mathrm{5}\right\} \\ $$$${y}=\left\{\mathrm{0},\mathrm{5},\mathrm{7},\mathrm{8},\mathrm{10}\right\} \\ $$

Question Number 7238 Answers: 0 Comments: 1

um numero somado ao seu triplo e igual a 36. qual e esse numero?

$${um}\:{numero}\:{somado}\:{ao}\:{seu}\:{triplo}\:{e}\:{igual}\:{a}\:\mathrm{36}.\:{qual}\:{e}\:{esse}\:{numero}? \\ $$

Question Number 7239 Answers: 0 Comments: 1

A soma de um numero com seu sextuplo e ingual a 280.Quale e o numero?

$${A}\:{soma}\:{de}\:{um}\:{numero}\:{com}\:{seu}\:{sextuplo}\:{e}\:{ingual}\:{a}\:\mathrm{280}.{Quale}\:{e}\:{o}\:{numero}? \\ $$

Question Number 7243 Answers: 0 Comments: 2

lim_(x→∞) ((√(x^2 +x+1)))−((√(x^2 +1))) <

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{\left.{x}^{\mathrm{2}} +{x}+\mathrm{1}\right)}−\left(\sqrt{\left.{x}^{\mathrm{2}} +\mathrm{1}\right)}\right.\right. \\ $$$$< \\ $$

Question Number 7031 Answers: 1 Comments: 5

Question Number 6830 Answers: 0 Comments: 0

A, B, and C are three non-collinear points such that ∣AB∣=c , ∣BC∣=a and ∣CA∣=b. What will be the condition for a point D to be concircle with A, B and C when all the four points belong to same plane?

$${A},\:{B},\:{and}\:{C}\:{are}\:{three}\:{non}-{collinear}\:{points}\:{such} \\ $$$${that}\:\mid{AB}\mid={c}\:,\:\mid{BC}\mid={a}\:\:{and}\:\:\mid{CA}\mid={b}. \\ $$$${What}\:{will}\:{be}\:{the}\:{condition}\:{for}\:{a}\:{point}\:{D}\:{to}\:{be} \\ $$$${concircle}\:{with}\:{A},\:{B}\:\:{and}\:{C}\:{when}\:{all}\:{the}\:{four} \\ $$$${points}\:{belong}\:{to}\:{same}\:{plane}? \\ $$

Question Number 6758 Answers: 0 Comments: 4

A circle of radius r has a point O as its centre. Points A and B are points on the circumference. For △OAB, OA^(−) =OB^(−) =r, AB^(−) =d, ∠AOB=θ. What is (r/d)?

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:{r}\:\mathrm{has}\:\mathrm{a}\:\mathrm{point}\:{O}\:\mathrm{as}\:\mathrm{its} \\ $$$$\mathrm{centre}.\:\mathrm{Points}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{circumference}. \\ $$$$ \\ $$$$\mathrm{For}\:\bigtriangleup{OAB},\:\overline {{OA}}=\overline {{OB}}={r},\:\overline {{AB}}={d},\:\angle{AOB}=\theta. \\ $$$$\mathrm{What}\:\mathrm{is}\:\frac{{r}}{{d}}? \\ $$

Question Number 6725 Answers: 0 Comments: 1

a+b=c a+a=ac c−a=b b+b=bc a^2 +b=c^3 a+D=b^2 b+D=a^2 a′b′+D=c′D ab+D=c_D ab+c=abc a′b′c′+D=D_(abc) abc+D=abc_D a^2 +b^± =Dab^(±2) (√(a^b +b^+_− ))=D^± (((a/b)+D))^(1/∂) =cot^(−1) a′b′

$${a}+{b}={c} \\ $$$${a}+{a}={ac} \\ $$$${c}−{a}={b} \\ $$$${b}+{b}={bc} \\ $$$${a}^{\mathrm{2}} +{b}={c}^{\mathrm{3}} \\ $$$${a}+{D}={b}^{\mathrm{2}} \\ $$$${b}+{D}={a}^{\mathrm{2}} \\ $$$${a}'{b}'+{D}={c}'{D} \\ $$$${ab}+{D}={c}_{{D}} \\ $$$${ab}+{c}={abc} \\ $$$${a}'{b}'{c}'+{D}={D}_{{abc}} \\ $$$${abc}+{D}={abc}_{{D}} \\ $$$${a}^{\mathrm{2}} +{b}^{\pm} ={Dab}^{\pm\mathrm{2}} \\ $$$$\sqrt{{a}^{{b}} +{b}^{+_{−} } }={D}^{\pm} \\ $$$$\sqrt[{\partial}]{\frac{{a}}{{b}}+{D}}=\mathrm{cot}^{−\mathrm{1}} {a}'{b}' \\ $$

Question Number 6640 Answers: 0 Comments: 4

ABC is a triangle,whose one vertex is moving along a circular path. Discuss the nature of the path, along which the centroid of the triangle is moving.

$$\mathrm{ABC}\:{is}\:{a}\:{triangle},{whose}\:{one}\:{vertex}\: \\ $$$${is}\:{moving}\:{along}\:{a}\:{circular}\:{path}.\: \\ $$$${Discuss}\:{the}\:{nature}\:{of}\:{the}\:\:{path},\:{along} \\ $$$${which}\:{the}\:\boldsymbol{{centroid}}\:{of}\:{the}\:{triangle} \\ $$$${is}\:{moving}. \\ $$

Question Number 6635 Answers: 1 Comments: 2

Question Number 6564 Answers: 1 Comments: 5

Let φ={ l_1 , l_2 , l_3 } be a set of three, nonparallel lines that all meet at one point R in the plane. Investigate conditions on φ such that R is the centroid of some triangle.

$${Let}\:\phi=\left\{\:{l}_{\mathrm{1}} \:,\:{l}_{\mathrm{2}} \:,\:{l}_{\mathrm{3}} \:\right\}\:{be}\:{a}\:{set}\:{of}\:{three},\:{nonparallel} \\ $$$${lines}\:{that}\:{all}\:{meet}\:{at}\:{one}\:{point}\:{R}\:{in}\: \\ $$$${the}\:{plane}.\:{Investigate}\:{conditions}\:{on}\:\phi \\ $$$${such}\:{that}\:{R}\:{is}\:{the}\:{centroid}\:{of}\:{some}\:{triangle}. \\ $$$$ \\ $$$$ \\ $$

Question Number 6553 Answers: 0 Comments: 10

Question Number 6488 Answers: 1 Comments: 7

Question Number 6475 Answers: 0 Comments: 3

Find a solution of the form ∅(x)=x^r Σ_(k=0) ^α c_k x^k (x > 0) for xy^(′′) + y′ − y = 0.

$${Find}\:{a}\:{solution}\:{of}\:{the}\:{form}\:\emptyset\left({x}\right)={x}^{{r}} \underset{{k}=\mathrm{0}} {\overset{\alpha} {\sum}}{c}_{{k}} {x}^{{k}} \:\left({x}\:>\:\mathrm{0}\right)\:{for}\: \\ $$$${xy}^{''} +\:{y}'\:−\:{y}\:=\:\mathrm{0}. \\ $$

Question Number 6419 Answers: 1 Comments: 0

Convert 34.8989898989 and 0.789789789789 to fraction.

$${Convert}\:\:\:\:\mathrm{34}.\mathrm{8989898989}\:\:\:\:{and}\:\:\:\:\mathrm{0}.\mathrm{789789789789}\: \\ $$$${to}\:{fraction}. \\ $$

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