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AllQuestion and Answers: Page 262

Question Number 195175 Answers: 1 Comments: 0

Question Number 195171 Answers: 0 Comments: 0

Question Number 195170 Answers: 2 Comments: 0

f(x)= { ((x^7 +2x+1 ;x≥2)),((x^2 +7x+4 ;x<1)) :} f^′ (1)=?

$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{7}} +\mathrm{2}{x}+\mathrm{1}\:\:\:\:\:\:\:;{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{4}\:\:\:\:\:\:\:\:;{x}<\mathrm{1}}\end{cases} \\ $$$${f}^{'} \left(\mathrm{1}\right)=? \\ $$

Question Number 195165 Answers: 0 Comments: 1

If r_1 ^(→) =(sinθ,cosθ,θ), r_2 ^(→) =(cosθ,−sinθ,−3) and r_3 ^(→) =(2,3,−1), find (d/dθ){r_1 ^(→) ×(r_2 ^(→) ×r_3 ^(→) )} at θ=0

$$\mathrm{If}\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{1}} }=\left(\mathrm{sin}\theta,\mathrm{cos}\theta,\theta\right),\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{2}} }=\left(\mathrm{cos}\theta,−\mathrm{sin}\theta,−\mathrm{3}\right)\:\mathrm{and} \\ $$$$\:\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }=\left(\mathrm{2},\mathrm{3},−\mathrm{1}\right),\:\mathrm{find}\:\frac{\mathrm{d}}{\mathrm{d}\theta}\left\{\overset{\rightarrow} {\mathrm{r}_{\mathrm{1}} }×\left(\overset{\rightarrow} {\mathrm{r}_{\mathrm{2}} }×\overset{\rightarrow} {\mathrm{r}_{\mathrm{3}} }\right)\right\}\:\mathrm{at}\:\theta=\mathrm{0} \\ $$

Question Number 195157 Answers: 1 Comments: 0

Prove that (x^3 /(2sin^2 ((1/2)arctan (x/y))))+(y^3 /(2cos^2 ((1/2)arctan (y/x))))=(x+y)(x^2 +y^2 )

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{x}^{\mathrm{3}} }{\mathrm{2}{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\:\frac{{x}}{{y}}\right)}+\frac{{y}^{\mathrm{3}} }{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\:\frac{{y}}{{x}}\right)}=\left({x}+{y}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right) \\ $$

Question Number 195154 Answers: 1 Comments: 0

lim_(x→2π) (((tan (π cos x))/(x^2 (x−5π)+4π^2 (2x−π))))=?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{2}\pi} {\mathrm{lim}}\:\left(\frac{\mathrm{tan}\:\left(\pi\:\mathrm{cos}\:{x}\right)}{{x}^{\mathrm{2}} \left({x}−\mathrm{5}\pi\right)+\mathrm{4}\pi^{\mathrm{2}} \left(\mathrm{2}{x}−\pi\right)}\right)=? \\ $$$$ \\ $$

Question Number 195148 Answers: 3 Comments: 0

determinant (((lim_(x→0) ((1+x sin x−cos x)/(sin^2 x))=?)))

$$\:\:\begin{array}{|c|}{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{x}\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}=?}\\\hline\end{array} \\ $$

Question Number 195137 Answers: 1 Comments: 0

f(x)=arctan(((4sinx)/(3+5cosx))) then f^′ ((π/3))=?

$${f}\left({x}\right)={arctan}\left(\frac{\mathrm{4}{sinx}}{\mathrm{3}+\mathrm{5}{cosx}}\right)\:\:\:{then}\:{f}^{'} \left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$

Question Number 195136 Answers: 1 Comments: 0

f(x)=arctan(sinx) and cosa=(2/3) faind f^′ (a)=?

$${f}\left({x}\right)={arctan}\left({sinx}\right) \\ $$$${and}\:\:{cosa}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\:\:\:{faind}\:\:\:{f}^{'} \left({a}\right)=? \\ $$

Question Number 195135 Answers: 4 Comments: 0

Question Number 195129 Answers: 3 Comments: 0

Calculer la valeur de la serie suivante: S=(3/2)+(5/8)+(7/(32))+(9/(128))+.....

$$\mathrm{Calculer}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\mathrm{la}\:\mathrm{serie}\:\mathrm{suivante}: \\ $$$$\boldsymbol{\mathrm{S}}=\frac{\mathrm{3}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{8}}+\frac{\mathrm{7}}{\mathrm{32}}+\frac{\mathrm{9}}{\mathrm{128}}+..... \\ $$

Question Number 195126 Answers: 1 Comments: 0

Soit f_n (x)=2^(n+1) [(((1/2^n )cotan((x/2^n ))−cotanx)/(sin((x/2^n ))))] Calculer lim_(x→0) f_n (x) et lim_(n→+∞) ((f_n (x))/2^(2n+2) )

$$\mathrm{Soit}\:{f}_{{n}} \left({x}\right)=\mathrm{2}^{{n}+\mathrm{1}} \left[\frac{\frac{\mathrm{1}}{\mathrm{2}^{{n}} }{cotan}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)−{cotanx}}{{sin}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)}\right] \\ $$$${Calculer}\:\underset{{x}\rightarrow\mathrm{0}} {{lim}f}_{{n}} \left({x}\right)\:{et}\:\underset{{n}\rightarrow+\infty} {{lim}}\:\frac{{f}_{{n}} \left({x}\right)}{\mathrm{2}^{\mathrm{2}{n}+\mathrm{2}} } \\ $$

Question Number 195124 Answers: 1 Comments: 0

Question Number 195120 Answers: 0 Comments: 0

Question Number 195118 Answers: 0 Comments: 1

a,b,c>0 & (1/a)+(1/b)+(1/c)=3 prove that (a/(b^2 +c^2 ))+(b/(a^2 +c^2 ))+(c/(a^2 +b^2 ))≥(3/2)(((a+b+c)/(ab+bc+ac)))^2

$${a},{b},{c}>\mathrm{0}\:\&\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{{a}}{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{b}}{{a}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{c}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\geqslant\frac{\mathrm{3}}{\mathrm{2}}\left(\frac{{a}+{b}+{c}}{{ab}+{bc}+{ac}}\right)^{\mathrm{2}} \\ $$

Question Number 195122 Answers: 0 Comments: 0

Question Number 195116 Answers: 0 Comments: 2

hi. please represntation (2)^(1/3) on number′s axis with ruler and compass and pen. thank you

$${hi}.\:{please}\:{represntation}\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:{on}\:{number}'{s}\:{axis} \\ $$$${with}\:{ruler}\:{and}\:{compass}\:{and}\:{pen}. \\ $$$${thank}\:{you} \\ $$

Question Number 195114 Answers: 2 Comments: 0

Σ_(k=3) ^(55) k=? 1)55 2)9k 3)53k 4)45

$$ \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\underset{\mathrm{k}=\mathrm{3}} {\overset{\mathrm{55}} {\sum}}\mathrm{k}=? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{9k}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{53k}\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{45} \\ $$$$ \\ $$$$ \\ $$

Question Number 195121 Answers: 2 Comments: 0

x^2 −x−1=0 x^8 +2x^7 −47x=?

$${x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$${x}^{\mathrm{8}} +\mathrm{2}{x}^{\mathrm{7}} −\mathrm{47}{x}=? \\ $$

Question Number 195107 Answers: 1 Comments: 0

Question Number 195101 Answers: 2 Comments: 0

(√(ln2)) >^? ln2

$$\sqrt{{ln}\mathrm{2}}\:\:\overset{?} {>}{ln}\mathrm{2} \\ $$

Question Number 195097 Answers: 1 Comments: 0

Question Number 195094 Answers: 1 Comments: 0

Question Number 195093 Answers: 2 Comments: 0

Question Number 195087 Answers: 2 Comments: 0

Question Number 195083 Answers: 1 Comments: 0

x=(√5)−2 x+(1/x)=?

$${x}=\sqrt{\mathrm{5}}−\mathrm{2}\:\:\:\:\: \\ $$$${x}+\frac{\mathrm{1}}{{x}}=? \\ $$

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