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Question Number 224017 Answers: 0 Comments: 0

x,y,z>0 xy+yz+zx+2xyz=1 prove that: (√(1−x^2 )) + (√(1−y^2 )) + (√(1−z^2 )) ≤ ((3 (√3))/2)

$$\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0} \\ $$$$\mathrm{xy}+\mathrm{yz}+\mathrm{zx}+\mathrm{2xyz}=\mathrm{1} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}−\mathrm{z}^{\mathrm{2}} }\:\leqslant\:\frac{\mathrm{3}\:\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$

Question Number 224016 Answers: 0 Comments: 0

a,b,c>0 a+b+c+2=abc prove that: (1/( (√(7+a)))) + (1/( (√(7+b)))) + (1/( (√(7+c)))) ≤ 1

$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{2}=\mathrm{abc} \\ $$$$\mathrm{prove}\:\mathrm{that}:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}+\mathrm{a}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}+\mathrm{b}}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}+\mathrm{c}}}\:\leqslant\:\mathrm{1} \\ $$

Question Number 224015 Answers: 0 Comments: 0

a,b,c>0 a+b+c+2=abc prove that: (√a) + (√b) + (√c) ≤ (3/2) (√(abc))

$$\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{2}=\mathrm{abc} \\ $$$$\mathrm{prove}\:\mathrm{that}:\:\:\:\sqrt{\mathrm{a}}\:+\:\sqrt{\mathrm{b}}\:+\:\sqrt{\mathrm{c}}\:\leqslant\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt{\mathrm{abc}} \\ $$

Question Number 224013 Answers: 1 Comments: 1

Question Number 223995 Answers: 1 Comments: 0

Question Number 223990 Answers: 5 Comments: 1

lim_(x→1) ((x(x+(1/x))^5 −32 )/(x−1))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{5}} −\mathrm{32}\:}{{x}−\mathrm{1}} \\ $$

Question Number 223988 Answers: 0 Comments: 0

Solve the DE using the method of Frobenius : (1−x^2 )y′′−2xy′+n(n+1)y=0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{DE}\:\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{Frobenius}\::\: \\ $$$$\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}''−\mathrm{2xy}'+\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)\mathrm{y}=\mathrm{0} \\ $$

Question Number 223978 Answers: 0 Comments: 5

Guys my exams are starting from today.Wish me luck!

$${Guys}\:{my}\:{exams}\:{are}\:{starting} \\ $$$${from}\:{today}.{Wish}\:{me}\:{luck}! \\ $$

Question Number 223965 Answers: 2 Comments: 0

Question Number 223964 Answers: 3 Comments: 0

Question Number 223962 Answers: 2 Comments: 1

Question Number 223958 Answers: 0 Comments: 0

∫_0 ^∞ ((x sinh(x))/(1+cosh^2 (x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{x}\:\mathrm{sinh}\left({x}\right)}{\mathrm{1}+\mathrm{cosh}^{\mathrm{2}} \left({x}\right)}\:\mathrm{d}{x} \\ $$$$ \\ $$

Question Number 223954 Answers: 2 Comments: 0

Question Number 224003 Answers: 2 Comments: 1

Question Number 223935 Answers: 3 Comments: 1

Question Number 223933 Answers: 1 Comments: 0

I=∫_0 ^1 ((ln(x+1))/(x^2 +1))dx

$${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({x}+\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 223928 Answers: 3 Comments: 1

Question Number 223923 Answers: 1 Comments: 0

find ∫_0 ^∞ ((ln(1+x))/(1+x^3 ))dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 223920 Answers: 1 Comments: 0

find ∫_0 ^(π/2) (x^2 /(sin^2 x))dx

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} }{{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 223917 Answers: 0 Comments: 0

Question Number 223908 Answers: 1 Comments: 0

Question Number 223901 Answers: 1 Comments: 2

Question Number 223889 Answers: 0 Comments: 2

Question Number 223887 Answers: 0 Comments: 2

Question Number 223881 Answers: 2 Comments: 0

Question Number 223865 Answers: 1 Comments: 1

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