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Question Number 35439 Answers: 0 Comments: 1

Question Number 35438 Answers: 0 Comments: 1

let m>0 and 0<a<b 1) calculate ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )(x^2 +b^2 )))dx 2)find the value of ∫_0 ^∞ ((cos(2x))/((x^2 +1)(x^2 +3)))dx

$${let}\:{m}>\mathrm{0}\:{and}\:\mathrm{0}<{a}<{b}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:\:+\mathrm{3}\right)}{dx} \\ $$

Question Number 35430 Answers: 1 Comments: 1

Question Number 35429 Answers: 1 Comments: 1

find ∫_0 ^1 ((2x−1)/(√(x^2 +6))) dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} \:\:+\mathrm{6}}}\:{dx} \\ $$

Question Number 35428 Answers: 1 Comments: 1

find ∫ ((x+3)/(√(x^2 +x −1)))dx

$${find}\:\:\:\:\:\int\:\:\:\:\frac{{x}+\mathrm{3}}{\sqrt{{x}^{\mathrm{2}} \:+{x}\:−\mathrm{1}}}{dx} \\ $$

Question Number 35427 Answers: 1 Comments: 1

calculate ∫_2 ^5 (e^(√(x+1)) /(√(x+1)))dx

$${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\frac{{e}^{\sqrt{{x}+\mathrm{1}}} }{\sqrt{{x}+\mathrm{1}}}{dx} \\ $$

Question Number 35425 Answers: 1 Comments: 0

Given that a number is a factor of 144 and the square of the number added to five times the number is ≥ −6 find the number

$$\:{Given}\:{that}\:{a}\:{number}\:{is}\:{a}\:{factor}\: \\ $$$${of}\:\mathrm{144}\:{and}\:{the}\:{square}\:{of}\:{the}\:{number} \\ $$$${added}\:{to}\:{five}\:{times}\:{the}\:{number} \\ $$$${is}\:\geqslant\:−\mathrm{6}\:{find}\:{the}\:{number} \\ $$

Question Number 35426 Answers: 1 Comments: 2

find the value of x if the inverse of the matrix (((x+5 2)),((7 x)) ) is (((0 0)),((0 0)) )

$${find}\:{the}\:{value}\:{of}\:{x}\:{if}\:{the}\:{inverse} \\ $$$${of}\:{the}\:{matrix}\:\begin{pmatrix}{{x}+\mathrm{5}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\:{is} \\ $$$$\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 35422 Answers: 0 Comments: 2

Question Number 35416 Answers: 1 Comments: 2

let −1≤x≤1 simplify A=sin{ arcsinx +2arcsin)(1−x)}

$${let}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{simplify} \\ $$$$\left.{A}={sin}\left\{\:{arcsinx}\:\:+\mathrm{2}{arcsin}\right)\left(\mathrm{1}−{x}\right)\right\} \\ $$

Question Number 35412 Answers: 1 Comments: 2

evaluate ∫(√((t^2 +1+(3/4)t))) dt

$$\boldsymbol{\mathrm{evaluate}}\:\int\sqrt{\left(\boldsymbol{\mathrm{t}}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}\boldsymbol{\mathrm{t}}\right)}\:\boldsymbol{\mathrm{dt}} \\ $$

Question Number 35646 Answers: 1 Comments: 2

Question Number 35645 Answers: 1 Comments: 0

sketch the graph of f(x)=2−x−x^2 then state its domain and range

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\mathrm{2}−\boldsymbol{{x}}−\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{state}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{domain}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{range}} \\ $$

Question Number 35390 Answers: 1 Comments: 6

Question Number 35384 Answers: 1 Comments: 1

((−1+i(√3)))^(1/6) =....??

$$\sqrt[{\mathrm{6}}]{−\mathrm{1}+{i}\sqrt{\mathrm{3}}}\:=....?? \\ $$

Question Number 35379 Answers: 2 Comments: 3

∫_0 ^( 1) t^2 (√(1+t^2 )) dt = ?

$$\int_{\mathrm{0}} ^{\:\:\mathrm{1}} {t}^{\mathrm{2}} \sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt}\:=\:? \\ $$

Question Number 35367 Answers: 2 Comments: 0

Q_(3 ) . a number is a factor of 6 the square of the number added to 5 times thenumber is same as −6 find the number.

$${Q}_{\mathrm{3}\:} .\:{a}\:{number}\:{is}\:{a}\:{factor}\:{of}\:\mathrm{6} \\ $$$$\:{the}\:{square}\:{of}\:{the}\:{number}\:{added}\: \\ $$$${to}\:\mathrm{5}\:{times}\:{thenumber}\:{is}\:{same}\:{as} \\ $$$$−\mathrm{6}\:{find}\:{the}\:{number}. \\ $$

Question Number 35362 Answers: 1 Comments: 3

Question Number 35363 Answers: 3 Comments: 0

Q_1 . A quadratic equation x^2 −3x+4=0 has roots α and β .without solving a)write down the values of α^2 +β^2 b) find the quadratic equation with integral coefficients,whose roots are (1/α^2 ) and(1/β^2 ) Q_2 . the first term of a GP is 32 and the sum to infinity is 48. find the common ratio and the 8^(th) term of the progression

$${Q}_{\mathrm{1}} .\:{A}\:{quadratic}\:{equation}\:{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{4}=\mathrm{0} \\ $$$${has}\:{roots}\:\alpha\:{and}\:\beta\:.{without}\:{solving} \\ $$$$\left.{a}\right){write}\:{down}\:{the}\:{values}\:{of}\:\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} \\ $$$$\left.{b}\right)\:{find}\:{the}\:{quadratic}\:{equation} \\ $$$${with}\:{integral}\:{coefficients},{whose} \\ $$$${roots}\:{are}\:\frac{\mathrm{1}}{\alpha^{\mathrm{2}} }\:{and}\frac{\mathrm{1}}{\beta^{\mathrm{2}} } \\ $$$${Q}_{\mathrm{2}} .\:{the}\:{first}\:{term}\:{of}\:{a}\:{GP}\:{is}\:\mathrm{32}\: \\ $$$${and}\:{the}\:{sum}\:{to}\:{infinity}\:{is}\:\mathrm{48}. \\ $$$${find}\:{the}\:{common}\:{ratio}\:{and}\:{the}\:\mathrm{8}^{{th}} \\ $$$${term}\:{of}\:{the}\:{progression} \\ $$

Question Number 35357 Answers: 2 Comments: 0

Q_1 . find the term in x^6 in the expansion of (x^2 +(2/x))^9 Q_2 . in the binomial expansion of (x+(k/x))^6 , the term independent of x is 160 find the value of k. Q_3 . find the constand term in the binomial of (x+(3/x))^(12) .

$${Q}_{\mathrm{1}} .\:{find}\:{the}\:{term}\:{in}\:{x}^{\mathrm{6}} \:{in}\:{the}\: \\ $$$${expansion}\:{of}\:\left({x}^{\mathrm{2}} +\frac{\mathrm{2}}{{x}}\right)^{\mathrm{9}} \\ $$$${Q}_{\mathrm{2}} .\:{in}\:{the}\:{binomial}\:{expansion}\:{of} \\ $$$$\:\left({x}+\frac{{k}}{{x}}\right)^{\mathrm{6}} ,\:{the}\:{term}\:{independent}\:{of}\:{x} \\ $$$${is}\:\mathrm{160}\:{find}\:{the}\:{value}\:{of}\:{k}. \\ $$$${Q}_{\mathrm{3}} .\:{find}\:{the}\:{constand}\:{term}\:{in}\:{the} \\ $$$${binomial}\:{of}\:\left({x}+\frac{\mathrm{3}}{{x}}\right)^{\mathrm{12}} . \\ $$

Question Number 35348 Answers: 0 Comments: 0

Question Number 35347 Answers: 3 Comments: 0

Question Number 35345 Answers: 0 Comments: 0

yes (√2)x^2

$${yes}\:\sqrt{\mathrm{2}}{x}^{\mathrm{2}} \\ $$

Question Number 35344 Answers: 0 Comments: 0

Question Number 35338 Answers: 0 Comments: 1

((14x^2 +16)/(21))−((2x^2 +8)/(8x^2 −11))=((2x^2 )/3)

$$\frac{\mathrm{14}{x}^{\mathrm{2}} +\mathrm{16}}{\mathrm{21}}−\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{8}}{\mathrm{8}{x}^{\mathrm{2}} −\mathrm{11}}=\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{3}} \\ $$

Question Number 35336 Answers: 2 Comments: 1

(√(2x^2 ))+7x+5(√2)=0

$$\sqrt{\mathrm{2}{x}^{\mathrm{2}} }+\mathrm{7}{x}+\mathrm{5}\sqrt{\mathrm{2}}=\mathrm{0} \\ $$

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