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Question Number 97460 Answers: 1 Comments: 2

Question Number 97454 Answers: 2 Comments: 0

Question Number 97439 Answers: 0 Comments: 2

∫_((√2)/2) ^1 ((x^3 /2) + (1/(6x)))(√(1+(((3x^2 )/2) −(1/(6x^2 )))^2 )) dx

$$\underset{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{6x}}\right)\sqrt{\mathrm{1}+\left(\frac{\mathrm{3x}^{\mathrm{2}} }{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{6x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 97438 Answers: 1 Comments: 1

If −3≤x≤4, −2≤y≤5, 4≤z≤10 , find the greatest value of w = z−xy

$$\mathrm{If}\:−\mathrm{3}\leqslant\mathrm{x}\leqslant\mathrm{4},\:−\mathrm{2}\leqslant\mathrm{y}\leqslant\mathrm{5},\:\mathrm{4}\leqslant\mathrm{z}\leqslant\mathrm{10} \\ $$$$,\:\mathrm{find}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{w}\:=\:\mathrm{z}−\mathrm{xy}\: \\ $$

Question Number 97423 Answers: 2 Comments: 0

solve y^(′′) +4y =xe^(−x) with y(0)=1 and y^′ (0) =−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{4y}\:=\mathrm{xe}^{−\mathrm{x}} \:\:\:\:\mathrm{with}\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$

Question Number 97428 Answers: 2 Comments: 5

Question Number 97418 Answers: 1 Comments: 1

Verify if the series Σ_(n=1) ^n ((2n + 5)/(n^2 +3n + 2)) is convergent or divergent. What method is easier?

$$\mathrm{Verify}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\: \\ $$$$\:\underset{{n}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}{n}\:+\:\mathrm{5}}{{n}^{\mathrm{2}} \:+\mathrm{3}{n}\:+\:\mathrm{2}}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}. \\ $$$$\mathrm{What}\:\mathrm{method}\:\mathrm{is}\:\mathrm{easier}? \\ $$

Question Number 97417 Answers: 1 Comments: 0

∫(x/(a+sin^2 x))dx=?

$$\int\frac{{x}}{{a}+\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=? \\ $$

Question Number 97413 Answers: 1 Comments: 0

Given that ω = e^(iθ) , θ≠ nπ , n ∈N show that (1 + ω)^n = 2^n ((1/2)θ)e^((1/2)(inθ)) please help me out on this, i′ve stumbled on it.

$$\mathrm{Given}\:\mathrm{that}\:\omega\:=\:{e}^{{i}\theta} ,\:\theta\neq\:{n}\pi\:,\:{n}\:\in\mathbb{N} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{1}\:+\:\omega\right)^{{n}} \:=\:\mathrm{2}^{{n}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right){e}^{\frac{\mathrm{1}}{\mathrm{2}}\left({in}\theta\right)} \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out}\:\mathrm{on}\:\mathrm{this},\:\mathrm{i}'\mathrm{ve}\:\mathrm{stumbled}\:\mathrm{on}\:\mathrm{it}. \\ $$

Question Number 97412 Answers: 2 Comments: 0

prove (√2)<log_2 3<(√3)

$${prove} \\ $$$$\sqrt{\mathrm{2}}<\mathrm{log}_{\mathrm{2}} \:\mathrm{3}<\sqrt{\mathrm{3}} \\ $$

Question Number 97403 Answers: 0 Comments: 1

Question Number 97401 Answers: 0 Comments: 1

Question Number 97400 Answers: 0 Comments: 2

∫((xdx)/(sin^2 x−3))=? help me

$$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$$$\:\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 97398 Answers: 0 Comments: 0

The discontinuty of [x]^2 −[x^2 ]

$$\mathrm{The}\:\mathrm{discontinuty}\:\mathrm{of}\:\left[\mathrm{x}\right]^{\mathrm{2}} −\left[\mathrm{x}^{\mathrm{2}} \right] \\ $$

Question Number 97390 Answers: 1 Comments: 0

compare log_2 3 with log_3 4

$${compare}\:{log}_{\mathrm{2}} \mathrm{3}\:{with}\:{log}_{\mathrm{3}} \mathrm{4} \\ $$

Question Number 97386 Answers: 0 Comments: 2

Question Number 97380 Answers: 0 Comments: 0

E is a vectorial plane. his base is B=(i^→ ;j^→ ). f is an endomorphism defined by f(i^→ )=−((√2)/2)i^→ +((√2)/2)j^→ and f(j^→ )=((√2)/2)i^→ −((√2)/2)j^→ 1)Show that ker f is a vectorial straigh line and his base is e_1 ^→ =(√2)i^→ +(√2)j^→ 2)show that G, the set of vectors u^→ ∈ E such as f(u^→ )=(√2)u^→ is a vectorial straigh line and his Base is e_(2 ) ^→ =i^→ +j^→ 3) Determine the matrix A′ of f in B′ if B′=(e_1 ^→ ;e_2 ^→ ).

Question Number 97371 Answers: 0 Comments: 1

Question Number 97369 Answers: 1 Comments: 0

∫_0 ^1 (((ln(x))^2 )/(1+x^2 ))dx=(π^3 /(16))

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left({ln}\left({x}\right)\right)^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi^{\mathrm{3}} }{\mathrm{16}} \\ $$

Question Number 97368 Answers: 3 Comments: 11

Question Number 97361 Answers: 1 Comments: 6

∫((xdx)/(sin^2 x−3))=?

$$\int\frac{\mathrm{xdx}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3}}=? \\ $$

Question Number 97355 Answers: 0 Comments: 1

Question Number 97353 Answers: 5 Comments: 0

Question Number 97346 Answers: 1 Comments: 0

Question Number 97335 Answers: 0 Comments: 2

Question Number 97323 Answers: 1 Comments: 0

Mr Peter has 4 children. x are in class C and y are in class D. x≥1 and y≥1. Show that the number of possibility to choose at random and simultaneous 2 children in same class verify this equation p(x)=x^2 −4x+6

$${Mr}\:{Peter}\:{has}\:\mathrm{4}\:{children}.\:{x}\:{are}\:{in}\: \\ $$$${class}\:{C}\:{and}\:{y}\:{are}\:{in}\:{class}\:{D}.\:{x}\geqslant\mathrm{1}\:{and} \\ $$$${y}\geqslant\mathrm{1}.\:{Show}\:{that}\:{the}\:{number}\:{of}\:{possibility}\: \\ $$$${to}\:{choose}\:{at}\:{random}\:{and}\:{simultaneous} \\ $$$$\mathrm{2}\:{children}\:{in}\:{same}\:{class}\:{verify}\:{this} \\ $$$${equation}\:{p}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{6} \\ $$

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