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Question Number 142150    Answers: 1   Comments: 1

Π_(n=1) ^∞ (1+(1/n^4 )) =?

$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)\:=?\: \\ $$

Question Number 142149    Answers: 5   Comments: 0

6. ∫(dx/(x^2 −3x+2)) 7. ∫((4dx)/(x^2 +2x+4)) 8. ∫((3−2xdx)/(x^2 −64)) 9. ∫((3x−1)/(x^3 +5x^2 +6x))dx 10. ∫((4−3x)/(x^3 −2x))dx 11. ∫(dx/(x^3 −2x+x))

$$\mathrm{6}.\:\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$$\mathrm{7}.\:\int\frac{\mathrm{4}{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$$$\mathrm{8}.\:\int\frac{\mathrm{3}−\mathrm{2}{xdx}}{{x}^{\mathrm{2}} −\mathrm{64}} \\ $$$$\mathrm{9}.\:\int\frac{\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}{x}}{dx} \\ $$$$\mathrm{10}.\:\int\frac{\mathrm{4}−\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{2}{x}}{dx} \\ $$$$\mathrm{11}.\:\int\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}+{x}} \\ $$$$ \\ $$

Question Number 142148    Answers: 1   Comments: 0

Σ_(n=0) ^∞ (1/(n!))=?

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}!}=? \\ $$

Question Number 142140    Answers: 1   Comments: 0

[lim_(x→0) ((sin x)/x)]=? lim_(x→0) {[((100sin^(−1) x)/x)]+[((100tan^(−1) x)/x)]}=? lim_(x→0) {[((100x)/(sin^(−1) x))]+[((100x)/(tan^(−1) x))]}=? where [x] denotes greatest integer less than or equal to x. solution please

$$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$$${solution}\:{please} \\ $$

Question Number 142138    Answers: 0   Comments: 6

(√(y^2 +1)) + (√(x^2 +4)) + (√(z^2 +9)) = 10 x+y+z=?

$$\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}\:+\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\:\sqrt{{z}^{\mathrm{2}} +\mathrm{9}}\:=\:\mathrm{10} \\ $$$${x}+{y}+{z}=? \\ $$

Question Number 142131    Answers: 1   Comments: 1

∫(dx/(3+2sinx+cosx))dx

$$\int\frac{{dx}}{\mathrm{3}+\mathrm{2}{sinx}+{cosx}}{dx} \\ $$

Question Number 142120    Answers: 2   Comments: 2

Question Number 142116    Answers: 2   Comments: 0

use trigonometric substitution to solve ∫(x^3 /( (√(9−x^2 ))))dx

$${use}\:{trigonometric}\:{substitution}\:{to}\:{solve} \\ $$$$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 142115    Answers: 2   Comments: 0

simplify A_n (x)=(1+ix)^n +(1−ix)^n x from C

$$\mathrm{simplify}\:\:\mathrm{A}_{\mathrm{n}} \left(\mathrm{x}\right)=\left(\mathrm{1}+\mathrm{ix}\right)^{\mathrm{n}} +\left(\mathrm{1}−\mathrm{ix}\right)^{\mathrm{n}} \:\:\:\mathrm{x}\:\mathrm{from}\:\mathrm{C} \\ $$

Question Number 142105    Answers: 2   Comments: 0

Sum the series to n terms sin θ−sin 2θ+sin 3θ−........

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms} \\ $$$$\mathrm{sin}\:\theta−\mathrm{sin}\:\mathrm{2}\theta+\mathrm{sin}\:\mathrm{3}\theta−........ \\ $$

Question Number 142269    Answers: 0   Comments: 0

Question Number 142268    Answers: 0   Comments: 0

∫(e^x /(cosx))dx

$$\int\frac{{e}^{{x}} }{{cosx}}{dx} \\ $$

Question Number 142100    Answers: 2   Comments: 0

∫^ (1/(1+(√(1+t)) )) dt=?

$$\:\:\:\:\:\:\int^{\:} \:\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{1}+{t}}\:}\:{dt}=? \\ $$

Question Number 142096    Answers: 0   Comments: 1

Question Number 142092    Answers: 0   Comments: 1

Question Number 142085    Answers: 2   Comments: 0

Proof that 1+3n<n^2 for every positive integer n≥4

$${Proof}\:{that}\:\mathrm{1}+\mathrm{3}{n}<{n}^{\mathrm{2}} \:{for}\:{every}\:{positive}\:{integer}\:{n}\geqslant\mathrm{4} \\ $$

Question Number 142079    Answers: 3   Comments: 0

y=(dy/dx)+(d^2 y/dx^2 )+(d^3 y/dx^3 )+..... solve this diffrential equation

$${y}=\frac{{dy}}{{dx}}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }+..... \\ $$$${solve}\:{this}\:{diffrential}\:{equation} \\ $$

Question Number 142061    Answers: 0   Comments: 3

(√(5x^2 +y^2 +z^2 +2x+2+2xy−4xz+10)) + ∣2x−y−13∣ = 3

$$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}+\mathrm{2}{xy}−\mathrm{4}{xz}+\mathrm{10}}\:+ \\ $$$$\mid\mathrm{2}{x}−{y}−\mathrm{13}\mid\:=\:\mathrm{3}\: \\ $$

Question Number 142060    Answers: 2   Comments: 0

Question Number 142045    Answers: 2   Comments: 0

Question Number 142041    Answers: 3   Comments: 0

Question Number 142052    Answers: 3   Comments: 0

Given that fog(x)=((2x−1)/x) and g(x)=5x+2, Find f(x).

$$\boldsymbol{\mathrm{Given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{fog}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{1}}{\boldsymbol{\mathrm{x}}}\:\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{5}\boldsymbol{\mathrm{x}}+\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right). \\ $$$$ \\ $$

Question Number 142049    Answers: 2   Comments: 0

∫_1 ^( 3) e^x^2 dx help me sir

$$\int_{\mathrm{1}} ^{\:\mathrm{3}} {e}^{{x}^{\mathrm{2}} } {dx} \\ $$$${help}\:{me}\:{sir}\: \\ $$

Question Number 142035    Answers: 1   Comments: 0

(1/2^(1/4) ).(3^(1/9) /4^(1/16) ).(5^(1/25) /6^(1/36) ).(7^(1/49) /8^(1/64) )...=exp(−((ζ′(2))/2)−(π^2 /(12))log (2))

$$\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}/\mathrm{4}} }.\frac{\mathrm{3}^{\mathrm{1}/\mathrm{9}} }{\mathrm{4}^{\mathrm{1}/\mathrm{16}} }.\frac{\mathrm{5}^{\mathrm{1}/\mathrm{25}} }{\mathrm{6}^{\mathrm{1}/\mathrm{36}} }.\frac{\mathrm{7}^{\mathrm{1}/\mathrm{49}} }{\mathrm{8}^{\mathrm{1}/\mathrm{64}} }...={exp}\left(−\frac{\zeta'\left(\mathrm{2}\right)}{\mathrm{2}}−\frac{\pi^{\mathrm{2}} }{\mathrm{12}}\mathrm{log}\:\left(\mathrm{2}\right)\right) \\ $$

Question Number 142036    Answers: 0   Comments: 0

Question Number 142028    Answers: 2   Comments: 0

............Calculus......... ∫_0 ^( ∞) ((sin(sin(x)).e^(cos(x)) )/x)dx=??? ............m.n.....

$$\:\:\:\:\:\:\:\:............{Calculus}.........\: \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({sin}\left({x}\right)\right).{e}^{{cos}\left({x}\right)} }{{x}}{dx}=??? \\ $$$$\:............{m}.{n}..... \\ $$

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