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AllQuestion and Answers: Page 667

Question Number 143208 Answers: 1 Comments: 0

3^x +4x−3=x^4 find x

$$\mathrm{3}^{{x}} +\mathrm{4}{x}−\mathrm{3}={x}^{\mathrm{4}} \\ $$$${find}\:{x} \\ $$

Question Number 143200 Answers: 1 Comments: 0

Question Number 143194 Answers: 1 Comments: 0

Suppose z^(50) +z^(25) +m=0, where z=((1+i)/( (√2))) find the value of m.

$$\mathrm{Suppose}\:{z}^{\mathrm{50}} +{z}^{\mathrm{25}} +{m}=\mathrm{0},\:\mathrm{where}\:{z}=\frac{\mathrm{1}+{i}}{\:\sqrt{\mathrm{2}}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{m}. \\ $$

Question Number 143193 Answers: 1 Comments: 0

prove that the function f(x)=x^2 ,xε[1,4] is Riemannian integral ?

$${prove}\:{that}\:{the}\:{function}\:{f}\left({x}\right)={x}^{\mathrm{2}} \:\:,{x}\varepsilon\left[\mathrm{1},\mathrm{4}\right] \\ $$$${is}\:{Riemannian}\:{integral}\:? \\ $$

Question Number 143192 Answers: 0 Comments: 0

Question Number 143191 Answers: 1 Comments: 0

Question Number 143190 Answers: 1 Comments: 2

∫_R (e^(its) /(s+3))ds

$$\int_{\mathbb{R}} \frac{\mathrm{e}^{\mathrm{its}} }{\mathrm{s}+\mathrm{3}}\mathrm{ds} \\ $$

Question Number 143186 Answers: 0 Comments: 2

Question Number 143184 Answers: 1 Comments: 0

((10)/(25))+((28)/(125))+((82)/(625))+... = ?

$$\:\:\:\:\frac{\mathrm{10}}{\mathrm{25}}+\frac{\mathrm{28}}{\mathrm{125}}+\frac{\mathrm{82}}{\mathrm{625}}+...\:=\:? \\ $$

Question Number 143178 Answers: 0 Comments: 2

∫_1 ^∞ ((x2^x +7)/(3^x +lnx+1))dx

$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{x2}^{\mathrm{x}} +\mathrm{7}}{\mathrm{3}^{\mathrm{x}} +\mathrm{lnx}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 143535 Answers: 0 Comments: 0

Question Number 143537 Answers: 1 Comments: 0

Question Number 143168 Answers: 2 Comments: 2

Question Number 143165 Answers: 2 Comments: 4

solve the differention equation x=p^3 −p+2 since:p=y′

$${solve}\:{the}\:{differention}\:{equation} \\ $$$${x}={p}^{\mathrm{3}} −{p}+\mathrm{2}\:\:\:{since}:{p}={y}' \\ $$

Question Number 143163 Answers: 0 Comments: 0

∫_(1/x) ^x^2 (dt/( (√(1+t^3 )))) =?

$$\int_{\frac{\mathrm{1}}{{x}}} ^{{x}^{\mathrm{2}} } \frac{{dt}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{3}} }}\:=? \\ $$

Question Number 143156 Answers: 1 Comments: 0

lim_(n→∞) (1/n)(1+2^(1/2) +......+n^(1/n) ) ?

$${lim}_{{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\left(\mathrm{1}+\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{2}}} +......+{n}^{\frac{\mathrm{1}}{{n}}} \right)\:\:? \\ $$

Question Number 143150 Answers: 0 Comments: 2

If α and β are the roots of the equation determinant (((x−cos θ),(−sin θ)),((sin θ),(x−cos θ))), find the value of α^n +β^n , where n∈N.

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\begin{vmatrix}{{x}−\mathrm{cos}\:\theta}&{−\mathrm{sin}\:\theta}\\{\mathrm{sin}\:\theta}&{{x}−\mathrm{cos}\:\theta}\end{vmatrix}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha^{{n}} +\beta^{{n}} ,\:\mathrm{where}\:{n}\in\mathbb{N}. \\ $$

Question Number 143148 Answers: 0 Comments: 0

find v_n =Σ_(k=0) ^n (1/(3k+1)) interms of H_n H_n =Σ_(k=1) ^n (1/k)

$$\mathrm{find}\:\mathrm{v}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{3k}+\mathrm{1}}\:\mathrm{interms}\:\mathrm{of}\:\mathrm{H}_{\mathrm{n}} \\ $$$$\mathrm{H}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{k}} \\ $$

Question Number 143147 Answers: 0 Comments: 1

montrer que lasuite U_n =(H_n /n^2 ) est bornee H_n =Σ_(k=1) ^n (1/n^2 )

$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{lasuite}\:\mathrm{U}_{\mathrm{n}} =\frac{\mathrm{H}_{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} }\:\mathrm{est}\:\mathrm{bornee} \\ $$$$\mathrm{H}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} } \\ $$

Question Number 143142 Answers: 1 Comments: 0

∫((x^2 −1)/(x^2 +1))∙(1/( (√(1+x^4 ))))dx

$$\int\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\centerdot\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }}\mathrm{dx} \\ $$

Question Number 143139 Answers: 0 Comments: 0

Let a,b,c > 0 and a+b+c = 3. Prove that (1+a^2 )(1+b^2 )(1+c^2 ) ≤ (1+(1/( (√(abc)))))^3

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{b}^{\mathrm{2}} \right)\left(\mathrm{1}+{c}^{\mathrm{2}} \right)\:\leqslant\:\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{abc}}}\right)^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 143138 Answers: 0 Comments: 0

Let a,b > 0 and a+b = 2. Prove that (1+a^2 )(1+b^2 ) ≤ (1+(1/( (√(ab)))))^2

$$\mathrm{Let}\:{a},{b}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}\:=\:\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{b}^{\mathrm{2}} \right)\:\leqslant\:\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{ab}}}\right)^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 143134 Answers: 1 Comments: 0

Question Number 143131 Answers: 2 Comments: 0

find the partial sums of Σ_(n=1) ^∞ (1/(n^2 (n+1)))

$${find}\:{the}\:{partial}\:{sums}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)} \\ $$

Question Number 143130 Answers: 1 Comments: 1

Question Number 143127 Answers: 2 Comments: 0

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