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Question Number 74997 Answers: 1 Comments: 1

Question Number 74995 Answers: 1 Comments: 1

find ∫_0 ^(π/2) Log cosx dx

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

Question Number 74994 Answers: 0 Comments: 6

Question Number 74980 Answers: 1 Comments: 0

Prove that for n∈N^∗ Σ_(p=0) ^(n−1) [x+(p/n)]=[nx]

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left[\mathrm{x}+\frac{\mathrm{p}}{\mathrm{n}}\right]=\left[\mathrm{nx}\right] \\ $$

Question Number 74970 Answers: 2 Comments: 13

x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 find x^4 +y^4 +z^4 =? x^5 +y^5 +z^5 =? x^6 +y^6 +z^6 =? ...... x^n +y^n +z^n =?

$${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{3} \\ $$$$ \\ $$$${find} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =? \\ $$$${x}^{\mathrm{5}} +{y}^{\mathrm{5}} +{z}^{\mathrm{5}} =? \\ $$$${x}^{\mathrm{6}} +{y}^{\mathrm{6}} +{z}^{\mathrm{6}} =? \\ $$$$...... \\ $$$${x}^{{n}} +{y}^{{n}} +{z}^{{n}} =? \\ $$

Question Number 74966 Answers: 1 Comments: 2

If sin 2A=λsin 2B Prove that ((tan (A+B))/(tan (A−B)))=((λ+1)/(λ−1)) .

$${If}\:\:\mathrm{sin}\:\mathrm{2}{A}=\lambda\mathrm{sin}\:\mathrm{2}{B} \\ $$$${Prove}\:{that}\:\:\frac{\mathrm{tan}\:\left({A}+{B}\right)}{\mathrm{tan}\:\left({A}−{B}\right)}=\frac{\lambda+\mathrm{1}}{\lambda−\mathrm{1}}\:. \\ $$

Question Number 74959 Answers: 1 Comments: 1

f(x)=∣x+5∣−∣x−2∣−∣x+6∣ find f′(x)

$${f}\left({x}\right)=\mid{x}+\mathrm{5}\mid−\mid{x}−\mathrm{2}\mid−\mid{x}+\mathrm{6}\mid \\ $$$$ \\ $$$${find}\:{f}'\left({x}\right) \\ $$

Question Number 74948 Answers: 1 Comments: 0

The hhpotenuse of a right angled triangle has its ends at the points (1,3) and (−4,1) . Find an equation of the legs (perpendicar sides) of the triangle.

$$\mathrm{The}\:\mathrm{hhpotenuse}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle} \\ $$$$\mathrm{has}\:\mathrm{its}\:\mathrm{ends}\:\mathrm{at}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{and}\:\left(−\mathrm{4},\mathrm{1}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{legs}\:\left(\mathrm{perpendicar}\right. \\ $$$$\left.\:\mathrm{sides}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}. \\ $$

Question Number 74947 Answers: 1 Comments: 0

Question Number 74945 Answers: 1 Comments: 1

Question Number 74933 Answers: 0 Comments: 1

differentiate the following functions a)f(x)=2x^5 coshx

$$\mathrm{differentiate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions} \\ $$$$\left.\mathrm{a}\right)\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}^{\mathrm{5}} \:\mathrm{coshx} \\ $$

Question Number 74978 Answers: 1 Comments: 1

Question Number 74923 Answers: 0 Comments: 3

Σ_(k=1) ^n k^3 =[((n(n+1) )/2)]^2

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{3}} =\left[\frac{{n}\left({n}+\mathrm{1}\right)\:}{\mathrm{2}}\right]^{\mathrm{2}} \\ $$

Question Number 74957 Answers: 0 Comments: 0

what is the exact difference between relation and function ??

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{difference}\:\mathrm{between} \\ $$$$\mathrm{relation}\:\mathrm{and}\:\mathrm{function}\:?? \\ $$

Question Number 74914 Answers: 1 Comments: 0

Can someone solve this question plz? solve the contour integral ∫_C (e^(iz) /z^3 ) dz where C is the circle ∣z∣=2

$${Can}\:{someone}\:{solve}\:{this}\:{question}\:{plz}? \\ $$$${solve}\:{the}\:{contour}\:{integral}\: \\ $$$$\int_{{C}} \:\frac{{e}^{{iz}} }{{z}^{\mathrm{3}} }\:{dz}\:{where}\:{C}\:{is}\:{the}\:{circle}\:\mid{z}\mid=\mathrm{2} \\ $$

Question Number 74912 Answers: 1 Comments: 0

{ ((x^2 =yz+1)),((y^2 =xz+2)),((z^2 =xy+3)) :} ⇒x+y+z=?

$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} =\boldsymbol{\mathrm{yz}}+\mathrm{1}}\\{\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\boldsymbol{\mathrm{xz}}+\mathrm{2}}\\{\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\boldsymbol{\mathrm{xy}}+\mathrm{3}}\end{cases}\:\:\:\:\Rightarrow\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}=? \\ $$

Question Number 74904 Answers: 0 Comments: 1

Question Number 74900 Answers: 0 Comments: 2

Question Number 74910 Answers: 1 Comments: 0

Explain a function with examples based on our daily life ?

$$\mathrm{Explain}\:\mathrm{a}\:\mathrm{function}\:\mathrm{with}\:\mathrm{examples}\:\mathrm{based} \\ $$$$\mathrm{on}\:\mathrm{our}\:\mathrm{daily}\:\mathrm{life}\:? \\ $$

Question Number 74891 Answers: 0 Comments: 4

Q. How will you define integrating constant C ? In how many ways can you define C ?

$$\mathrm{Q}.\:\mathrm{How}\:\mathrm{will}\:\mathrm{you}\:\mathrm{define}\:\mathrm{integrating}\: \\ $$$$\mathrm{constant}\:\mathrm{C}\:?\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{you} \\ $$$$\mathrm{define}\:\mathrm{C}\:? \\ $$$$ \\ $$

Question Number 74890 Answers: 1 Comments: 1

find ∫ (x+3)(√((x−1)(2−x)))dx

$${find}\:\int\:\:\:\left({x}+\mathrm{3}\right)\sqrt{\left({x}−\mathrm{1}\right)\left(\mathrm{2}−{x}\right)}{dx} \\ $$

Question Number 74889 Answers: 1 Comments: 1

find ∫_(−(1/2)) ^(+∞) e^(−x) (√(2x+1))dx

$${find}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{+\infty} \:\:{e}^{−{x}} \sqrt{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$

Question Number 74888 Answers: 1 Comments: 3

calculate f(α)=∫(√(x^2 −x+α))dx (α real)

$${calculate}\:{f}\left(\alpha\right)=\int\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}{dx}\:\:\left(\alpha\:{real}\right) \\ $$

Question Number 74887 Answers: 0 Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/((n+1)n^3 ))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){n}^{\mathrm{3}} } \\ $$

Question Number 74886 Answers: 0 Comments: 1

calculate ∫ ((x+1)/((x^3 +x−2)^2 ))dx

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

Question Number 74885 Answers: 1 Comments: 0

calcilate Σ_(n=1) ^(16) (1/n^3 )

$${calcilate}\:\sum_{{n}=\mathrm{1}} ^{\mathrm{16}} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$

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