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Question Number 66401 Answers: 0 Comments: 0

Question Number 66399 Answers: 0 Comments: 1

Show that for all real values of x; x^(2/3) + 6x^(1/3) + 10 >0

$${Show}\:{that}\:{for}\:{all}\:{real} \\ $$$${values}\:{of}\:{x};\: \\ $$$$\:\:{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:+\:\mathrm{6}{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:\mathrm{10}\:>\mathrm{0} \\ $$

Question Number 66396 Answers: 1 Comments: 0

Seja 53^(log_(1/(√e^𝛑 )) [(((x+11)!))^(1/(9999999)) ]) = 1. Calcule (x_1 /x_2 )+0,9.

$$\: \\ $$$$\:\boldsymbol{\mathrm{Seja}}\:\:\mathrm{53}^{\boldsymbol{\mathrm{log}}_{\frac{\mathrm{1}}{\sqrt{\boldsymbol{{e}}^{\boldsymbol{\pi}} }}} \left[\sqrt[{\mathrm{9999999}}]{\left(\boldsymbol{{x}}+\mathrm{11}\right)!}\right]} \:=\:\mathrm{1}. \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Calcule}}\:\:\frac{\boldsymbol{\mathrm{x}}_{\mathrm{1}} }{\boldsymbol{\mathrm{x}}_{\mathrm{2}} }+\mathrm{0},\mathrm{9}. \\ $$

Question Number 66413 Answers: 1 Comments: 0

(√(8+log_6 (x!)))+(√(17−log_(x!) (6))) = 7

$$\: \\ $$$$\:\:\sqrt{\mathrm{8}+\boldsymbol{\mathrm{log}}_{\mathrm{6}} \left(\boldsymbol{\mathrm{x}}!\right)}+\sqrt{\mathrm{17}−\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}!} \left(\mathrm{6}\right)}\:=\:\mathrm{7} \\ $$$$\: \\ $$

Question Number 66412 Answers: 1 Comments: 3

if f(x)=ln(x+(√(x^2 +1))) find f^(−1) (x)=?

$${if} \\ $$$$ \\ $$$${f}\left({x}\right)={ln}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$${find} \\ $$$$ \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 66382 Answers: 0 Comments: 14

Give me any Quintic, i shall solve it. For sure! At^5 +Bt^4 +Ct^3 +Dt^2 +Et+F=0 wont even assume A=1, or B=0. but if A+C+E=B+D+F then my formula dont work but then obviously t=−1 is a root!

$${Give}\:{me}\:{any}\:{Quintic},\:{i}\:{shall}\:{solve} \\ $$$${it}.\:{For}\:{sure}! \\ $$$${At}^{\mathrm{5}} +{Bt}^{\mathrm{4}} +{Ct}^{\mathrm{3}} +{Dt}^{\mathrm{2}} +{Et}+{F}=\mathrm{0} \\ $$$${wont}\:{even}\:{assume}\:{A}=\mathrm{1},\:{or}\:{B}=\mathrm{0}. \\ $$$${but}\:{if}\:{A}+{C}+{E}={B}+{D}+{F}\: \\ $$$${then}\:{my}\:{formula}\:{dont}\:{work} \\ $$$${but}\:{then}\:{obviously}\:{t}=−\mathrm{1}\:{is}\:{a}\:{root}! \\ $$

Question Number 66379 Answers: 0 Comments: 2

Question Number 66381 Answers: 0 Comments: 0

Question Number 66356 Answers: 1 Comments: 0

Question Number 66355 Answers: 0 Comments: 1

Value of x satiesfied y=((log_4 (x^2 −1))/(4x^2 +2x+1)) negative value is... a. −1<x<(√2) b. −(√2)<x<1 c. −(√2)<x<(√2) d. −(√2)<x<−1 e. x<−2

$${V}\mathrm{alue}\:\mathrm{of}\:{x}\:\mathrm{satiesfied}\:{y}=\frac{\mathrm{log}_{\mathrm{4}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)}{\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}} \\ $$$${negative}\:{value}\:\mathrm{is}... \\ $$$$\mathrm{a}.\:−\mathrm{1}<{x}<\sqrt{\mathrm{2}} \\ $$$${b}.\:−\sqrt{\mathrm{2}}<{x}<\mathrm{1} \\ $$$${c}.\:−\sqrt{\mathrm{2}}<{x}<\sqrt{\mathrm{2}} \\ $$$${d}.\:−\sqrt{\mathrm{2}}<{x}<−\mathrm{1} \\ $$$${e}.\:{x}<−\mathrm{2} \\ $$

Question Number 66354 Answers: 0 Comments: 1

If 2x+y=8 and (x+y)=(3/2)log_(10) 2.log_8 36 then x^2 +3y=... a. 28 b. 22 c. 20 d. 16 e. 12

$$\mathrm{If}\:\:\mathrm{2}{x}+{y}=\mathrm{8}\:\mathrm{and} \\ $$$$\left({x}+{y}\right)=\frac{\mathrm{3}}{\mathrm{2}}\mathrm{log}_{\mathrm{10}} \:\mathrm{2}.\mathrm{log}_{\mathrm{8}} \mathrm{36} \\ $$$$\mathrm{then}\:\mathrm{x}^{\mathrm{2}} +\mathrm{3y}=... \\ $$$$\mathrm{a}.\:\mathrm{28} \\ $$$$\mathrm{b}.\:\mathrm{22} \\ $$$$\mathrm{c}.\:\mathrm{20} \\ $$$$\mathrm{d}.\:\mathrm{16} \\ $$$$\mathrm{e}.\:\mathrm{12} \\ $$

Question Number 66351 Answers: 0 Comments: 1

let I_n =∫_0 ^∞ (e^(nt) /((1+e^t )^(n+1) ))dt (n from N^★ ) )prove the existence of I_n 2)find lim_(n→+∞) I_n

$${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{{nt}} }{\left(\mathrm{1}+{e}^{{t}} \right)^{{n}+\mathrm{1}} }{dt}\:\:\:\:\:\left({n}\:{from}\:{N}^{\bigstar} \right) \\ $$$$\left.\right){prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:{I}_{{n}} \\ $$

Question Number 66350 Answers: 0 Comments: 1

study the convergence of ∫_0 ^∞ (1−(√(x^n /(2+x^n ))))dx n∈N

$${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\sqrt{\frac{{x}^{{n}} }{\mathrm{2}+{x}^{{n}} }}\right){dx}\:\:\:\:{n}\in{N} \\ $$

Question Number 66349 Answers: 0 Comments: 1

study the convergence of ∫_1 ^(+∞) ((arctan(x−1))/((x^2 −1)^(4/3) ))dx

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }{dx} \\ $$

Question Number 66348 Answers: 0 Comments: 0

find nature of ∫_0 ^1 (dx/(e^x −cosx))

$${find}\:{nature}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{e}^{{x}} −{cosx}} \\ $$

Question Number 66347 Answers: 0 Comments: 0

let I_n =∫_0 ^1 ((x^(2n+1) ln(x))/(x^2 −1))dx 1) prove the existence of I_n 2)calculate I_(n+1) −I_n 3)prove thst x∈]0,1[ ⇒0<((xlnx)/(x^2 −1))<(1/2) 4) find lim_(n→+∞) I_n

$${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} {ln}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right){prove}\:{thst}\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xlnx}}{{x}^{\mathrm{2}} −\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\right. \\ $$$$\left.\mathrm{4}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{I}_{{n}} \\ $$

Question Number 66346 Answers: 0 Comments: 2

find ∫_0 ^∞ (t^7 /(t^(16) +1))dt

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{7}} }{{t}^{\mathrm{16}} \:+\mathrm{1}}{dt} \\ $$

Question Number 66345 Answers: 0 Comments: 1

find the value of ∫_(−∞) ^(+∞) (dt/((t^2 −2t +2)^(3/2) ))

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

Question Number 66344 Answers: 0 Comments: 1

let f_n (x)=(1/((1+x^n )^(1+(1/n)) )) defined on [0,1] 1)prove that f_n →^(cs) to a function f on[0,1] 2) calculate I_n =∫_0 ^1 f_n (x)dx

$${let}\:{f}_{{n}} \left({x}\right)=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{{n}} \right)^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} }\:\:\:{defined}\:{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:{f}_{{n}} \rightarrow^{{cs}} \:\:{to}\:{a}\:{function}\:{f}\:{on}\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx} \\ $$

Question Number 66342 Answers: 0 Comments: 0

let U_n =∫_n ^(n+2) (((t+n)^(1/4) )/t^(1/3) )dt prove that lim_(n→+∞) U_n =0