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Question Number 39142 Answers: 1 Comments: 0

F(x) = x^3 −9x^2 +24x+c=0 has three real and distinct roots α , β & γ . Q.1 → Possible value of c is : Q.2 → If [α]+[β]+[γ]= 8 then c is : Q.3 → If [α]+[β]+[γ]=7 then c is : Options for the above 3 Q. → a) (−20,−16) b) (−20,−18) c) (−18,−16) d) none of these. [.] = greatest integer function.

$$\mathrm{F}\left({x}\right)\:=\:{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{24}{x}+{c}=\mathrm{0}\:{has}\:\mathrm{three} \\ $$$$\mathrm{real}\:\mathrm{and}\:\mathrm{distinct}\:\mathrm{roots}\:\alpha\:,\:\beta\:\&\:\gamma\:. \\ $$$$\mathrm{Q}.\mathrm{1}\:\rightarrow\:\mathrm{Possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{2}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\:\mathrm{8}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{3}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\mathrm{7}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$ \\ $$$$\mathrm{Options}\:\mathrm{for}\:\mathrm{the}\:\mathrm{above}\:\mathrm{3}\:\mathrm{Q}.\:\rightarrow \\ $$$$\left.\mathrm{a}\left.\right)\:\left(−\mathrm{20},−\mathrm{16}\right)\:\:\:\:\:\:\:\:\mathrm{b}\right)\:\left(−\mathrm{20},−\mathrm{18}\right) \\ $$$$\left.\mathrm{c}\left.\right)\:\left(−\mathrm{18},−\mathrm{16}\right)\:\:\:\:\:\:\:\:\:\mathrm{d}\right)\:\mathrm{none}\:\mathrm{of}\:\mathrm{these}. \\ $$$$ \\ $$$$\left[.\right]\:=\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$

Question Number 39135 Answers: 1 Comments: 2

calculate A(λ) = ∫_0 ^λ ((ln(x+(√(1+x^2 ))))/(√(1+x^2 ))) dx 2) calculate ∫_0 ^1 ((ln(x+(√(1+x^2 ))))/(√(1+x^2 )))dx

$${calculate}\:{A}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\lambda} \:\:\:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 39127 Answers: 0 Comments: 1

Given the lines l_1 : x + y = 5 and l_2 : y = 4x and l_3 ; 4x + y − 1 =0 show that l_(2 ) is perpendicular to l_3 . find the point coordinates if x + 2y = 5 is colliner to l_1

$${Given}\:{the}\:{lines} \\ $$$${l}_{\mathrm{1}} :\:\:{x}\:+\:{y}\:=\:\mathrm{5}\:{and}\:{l}_{\mathrm{2}} :\:{y}\:=\:\mathrm{4}{x} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:\mathrm{4}{x}\:+\:{y}\:−\:\mathrm{1}\:=\mathrm{0} \\ $$$${show}\:{that}\:{l}_{\mathrm{2}\:} \:{is}\:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{3}} . \\ $$$${find}\:{the}\:{point}\:{coordinates} \\ $$$${if}\:{x}\:+\:\mathrm{2}{y}\:=\:\mathrm{5}\:{is}\:{colliner}\:{to}\:{l}_{\mathrm{1}} \\ $$

Question Number 39144 Answers: 1 Comments: 0

f(x) = 3x^3 − 2x + k has factor (x − 1) find the value of k. with these value evaluate a) (d/(dx ))(f(x)_ ) b) ∫_5 ^2 (f(x))

$${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:\mathrm{2}{x}\:+\:{k}\:{has}\: \\ $$$${factor}\:\left({x}\:−\:\mathrm{1}\right)\:\: \\ $$$${find}\:{the}\:{value}\:{of}\:{k}. \\ $$$${with}\:{these}\:{value}\: \\ $$$${evaluate} \\ $$$$\left.{a}\right)\:\frac{{d}}{{dx}\:}\left({f}\left({x}\right)_{} \right) \\ $$$$\left.{b}\right)\:\int_{\mathrm{5}} ^{\mathrm{2}} \left({f}\left({x}\right)\right) \\ $$

Question Number 39121 Answers: 0 Comments: 5

Find domain of (1+(1/x))^x ? Also prove thatL_(x→0^+ ) (1+(1/x))^x = 1 ?

$$\mathrm{Find}\:\mathrm{domain}\:\mathrm{of}\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \:? \\ $$$$\mathrm{Also}\:\mathrm{prove}\:\mathrm{that}\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{L}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \:=\:\mathrm{1}\:? \\ $$

Question Number 39120 Answers: 1 Comments: 1

let A_n = ∫_1 ^n (([(√(1+x^2 ))] −[x])/x^2 ) dx (n integr ≥1) 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right]\:−\left[{x}\right]}{{x}^{\mathrm{2}} }\:{dx}\:\:\left({n}\:{integr}\:\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \\ $$

Question Number 39119 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 cos(4x))/((x^2 +1)^2 ))dx