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Question Number 169826 Answers: 1 Comments: 0

Given f(x)=(√(sin x)) +(√(3 cos x)) x∈ (0, (π/2)) Find max f(x).

$$\:\:{Given}\:{f}\left({x}\right)=\sqrt{\mathrm{sin}\:{x}}\:+\sqrt{\mathrm{3}\:\mathrm{cos}\:{x}}\: \\ $$$$\:\:{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\:{Find}\:{max}\:{f}\left({x}\right).\: \\ $$

Question Number 169825 Answers: 1 Comments: 0

Question Number 169821 Answers: 2 Comments: 0

Question Number 169815 Answers: 1 Comments: 8

Question Number 169812 Answers: 0 Comments: 0

Show that f(z)=z^2 is harmonic in the polar form Mastermind

$${Show}\:{that}\:{f}\left({z}\right)={z}^{\mathrm{2}} \:{is}\:{harmonic}\:{in}\:{the} \\ $$$${polar}\:{form} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169811 Answers: 0 Comments: 0

Show that f(z)=z is harmonic in the polar form Mastermind

$${Show}\:{that}\:{f}\left({z}\right)={z}\:{is}\:{harmonic}\:{in}\:{the} \\ $$$${polar}\:{form} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169809 Answers: 0 Comments: 1

prove that ∫_0 ^( ∞) x^r . e^(ax) dx = (−a)^(−r−1) .Γ(r+1)

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\:\infty} {x}^{{r}} \:.\:{e}^{{ax}} \:{dx}\:=\:\left(−{a}\right)^{−{r}−\mathrm{1}} \:.\Gamma\left({r}+\mathrm{1}\right) \\ $$

Question Number 169803 Answers: 1 Comments: 0

Question Number 169802 Answers: 1 Comments: 0

Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. a. Find the probability that a student’s total scores will be i. Greater than 850 ii. Less than 550 iii. Between 300 and 490

$$ \\ $$Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. a. Find the probability that a student’s total scores will be i. Greater than 850 ii. Less than 550 iii. Between 300 and 490

Question Number 169800 Answers: 0 Comments: 0

soit f(x,y)=x^5 y^2 (x−y) montrer q ue f est differentiable au point a=(2−1) applique en h=(1,1)

$${soit}\:{f}\left({x},{y}\right)={x}^{\mathrm{5}} {y}^{\mathrm{2}} \left({x}−{y}\right) \\ $$$${montrer}\:{q}\:{ue}\:{f}\:{est}\:{differentiable}\:{au}\:{point}\:{a}=\left(\mathrm{2}−\mathrm{1}\right) \\ $$$${applique}\:{en}\:{h}=\left(\mathrm{1},\mathrm{1}\right) \\ $$

Question Number 169798 Answers: 0 Comments: 2

log_e (e^2 x^(lnx) )=log_e (x^3 ) faind x=?

$${log}_{{e}} \left({e}^{\mathrm{2}} {x}^{{lnx}} \right)={log}_{{e}} \left({x}^{\mathrm{3}} \right) \\ $$$${faind}\:\:{x}=? \\ $$

Question Number 169797 Answers: 3 Comments: 0

Calculate for n∈ N^∗ :∫_0 ^(+∞) (dt/((t^2 +1)^n )) (Notice: 1=(1+t^2 )−t^2 )

$${Calculate}\:{for}\:{n}\in\:\mathbb{N}^{\ast} :\int_{\mathrm{0}} ^{+\infty} \frac{{dt}}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{{n}} } \\ $$$$\left({Notice}:\:\mathrm{1}=\left(\mathrm{1}+{t}^{\mathrm{2}} \right)−{t}^{\mathrm{2}} \right) \\ $$

Question Number 169792 Answers: 1 Comments: 0

f is continuous on R^+ such that ∫_0 ^(+∞) f(t)dt is convergent. Determinate lim_(x→+∞) ∫_x ^x^2 f(t)dt.

$${f}\:{is}\:{continuous}\:{on}\:\mathbb{R}^{+} \:{such}\:{that} \\ $$$$\int_{\mathrm{0}} ^{+\infty} {f}\left({t}\right){dt}\:{is}\:{convergent}. \\ $$$${Determinate}\:\underset{{x}\rightarrow+\infty} {{lim}}\int_{{x}} ^{{x}^{\mathrm{2}} } {f}\left({t}\right){dt}. \\ $$

Question Number 169790 Answers: 0 Comments: 0

Question Number 169768 Answers: 0 Comments: 0

[x]+[x+(1/2)]+[x−(1/3)]= 8 [2x]=8−[x−(1/3)]=k (k/2)≤x<((k+1)/2) , 8−k+(1/3)≤x <9−k+(1/3) (k/2) < ((28−3k)/3) ⇒ 9k < 56 k <((56)/9) ★ ((25)/3) −k<((k+1)/2) ⇒ 50−6k<3k+3 ⇒ ((47)/9) <x ★★ ★ & ★★ : k=6 3≤x< (7/2) (1) (7/3)≤x< ((10)/3) (2) (1) & (2) ⇒ (7/3)≤x<((10)/3)

$$\:\:\: \\ $$$$\:\:\:\left[{x}\right]+\left[{x}+\frac{\mathrm{1}}{\mathrm{2}}\right]+\left[{x}−\frac{\mathrm{1}}{\mathrm{3}}\right]=\:\mathrm{8} \\ $$$$\:\:\:\:\:\left[\mathrm{2}{x}\right]=\mathrm{8}−\left[{x}−\frac{\mathrm{1}}{\mathrm{3}}\right]={k} \\ $$$$\:\:\:\:\:\:\:\:\:\frac{{k}}{\mathrm{2}}\leqslant{x}<\frac{{k}+\mathrm{1}}{\mathrm{2}}\:,\:\:\:\:\:\mathrm{8}−{k}+\frac{\mathrm{1}}{\mathrm{3}}\leqslant{x}\:<\mathrm{9}−{k}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\frac{{k}}{\mathrm{2}}\:<\:\frac{\mathrm{28}−\mathrm{3}{k}}{\mathrm{3}}\:\:\Rightarrow\:\mathrm{9}{k}\:<\:\mathrm{56} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{k}\:<\frac{\mathrm{56}}{\mathrm{9}}\:\:\:\:\bigstar \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{25}}{\mathrm{3}}\:−{k}<\frac{{k}+\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{50}−\mathrm{6}{k}<\mathrm{3}{k}+\mathrm{3} \\ $$$$\:\:\:\:\Rightarrow\:\:\:\:\:\frac{\mathrm{47}}{\mathrm{9}}\:<{x}\:\:\bigstar\bigstar \\ $$$$\:\:\:\bigstar\:\:\&\:\bigstar\bigstar\::\:\:\:\:\:{k}=\mathrm{6} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\leqslant{x}<\:\frac{\mathrm{7}}{\mathrm{2}}\:\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{7}}{\mathrm{3}}\leqslant{x}<\:\frac{\mathrm{10}}{\mathrm{3}}\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\left(\mathrm{1}\right)\:\&\:\left(\mathrm{2}\right)\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:\frac{\mathrm{7}}{\mathrm{3}}\leqslant{x}<\frac{\mathrm{10}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 169765 Answers: 0 Comments: 3