Question and Answers Forum

All Questions Topic List

AllQuestion and Answers: Page 720

Question Number 145829 Answers: 1 Comments: 0

Question Number 145803 Answers: 1 Comments: 1

Question Number 145801 Answers: 2 Comments: 0

Question Number 145800 Answers: 0 Comments: 0

Question Number 145799 Answers: 0 Comments: 0

Question Number 145791 Answers: 1 Comments: 2

find lim_(x→0) ∫_0 ^x ((e^t +e^(−t) −2)/(1−cosx))dx

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\mathrm{x}} \:\frac{\mathrm{e}^{\mathrm{t}} +\mathrm{e}^{−\mathrm{t}} −\mathrm{2}}{\mathrm{1}−\mathrm{cosx}}\mathrm{dx} \\ $$

Question Number 145783 Answers: 2 Comments: 0

Question Number 145781 Answers: 1 Comments: 0

consider f(x)=Ax^2 +Bx+C with A>0. Show that f(x)≥0 ∀x iff B^2 −4AC≤0

$${consider}\:{f}\left({x}\right)={Ax}^{\mathrm{2}} +{Bx}+{C} \\ $$$${with}\:{A}>\mathrm{0}.\:{Show}\:{that}\:{f}\left({x}\right)\geqslant\mathrm{0}\:\forall{x}\:\:{iff}\: \\ $$$${B}^{\mathrm{2}} −\mathrm{4}{AC}\leqslant\mathrm{0} \\ $$

Question Number 145780 Answers: 1 Comments: 0

find the volume of the solid generated by the region bounded by y=(√x) , 0≤x≤1 and X−axis

$${find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\: \\ $$$${generated}\:{by}\:{the}\:{region}\:{bounded}\:{by} \\ $$$${y}=\sqrt{{x}}\:,\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:{X}−{axis} \\ $$

Question Number 145779 Answers: 1 Comments: 0

lim_(x→0) ∫_0 ^1 (e^t +e^(−t) −2)(dt/(1−cosx))

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\int_{\mathrm{0}} ^{\mathrm{1}} \left({e}^{{t}} +{e}^{−{t}} −\mathrm{2}\right)\frac{{dt}}{\mathrm{1}−{cosx}} \\ $$

Question Number 145777 Answers: 2 Comments: 0

∫(1/( (√(1−9x^2 ))))dx

$$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 145776 Answers: 2 Comments: 0

∫_0 ^(π/2) e^x cosxdx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {e}^{{x}} {cosxdx} \\ $$

Question Number 145775 Answers: 2 Comments: 0

∫((2x+1)/( (√(x^2 +4x+5))))dx

$$\int\frac{\mathrm{2}{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$

Question Number 145772 Answers: 0 Comments: 0

a;b;c>0 ; a^2 +b^2 +c^2 =2 prove: (a^6 +b^6 +c^6 )^3 ≥ (a^5 +b^5 +c^5 )^4

$${a};{b};{c}>\mathrm{0}\:;\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{2}\:{prove}: \\ $$$$\left({a}^{\mathrm{6}} +{b}^{\mathrm{6}} +{c}^{\mathrm{6}} \right)^{\mathrm{3}} \:\geqslant\:\left({a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{c}^{\mathrm{5}} \right)^{\mathrm{4}} \\ $$

Question Number 145774 Answers: 1 Comments: 0

find the area bounded by y=2x, y=(x/2) and?xy=2

$${find}\:{the}\:{area}\:{bounded}\:{by}\:{y}=\mathrm{2}{x},\:{y}=\frac{{x}}{\mathrm{2}}\:{and}?{xy}=\mathrm{2} \\ $$

Question Number 145773 Answers: 1 Comments: 0

Question Number 145769 Answers: 1 Comments: 1

find x if 2^x +2^(3x) =16

$${find}\:{x}\:{if}\:\:\mathrm{2}^{{x}} +\mathrm{2}^{\mathrm{3}{x}} =\mathrm{16} \\ $$

Question Number 145768 Answers: 0 Comments: 0

x;y;z;t∈Z^+ { ((xy + zt = 38)),((xz + yt = 34)),((xt + yz = 43)) :} ⇒ x+y+z+t=?

$${x};{y};{z};{t}\in\mathbb{Z}^{+} \\ $$$$\begin{cases}{{xy}\:+\:{zt}\:=\:\mathrm{38}}\\{{xz}\:+\:{yt}\:=\:\mathrm{34}}\\{{xt}\:+\:{yz}\:=\:\mathrm{43}}\end{cases}\:\:\Rightarrow\:{x}+{y}+{z}+{t}=? \\ $$

Question Number 145766 Answers: 0 Comments: 0

Question Number 145760 Answers: 0 Comments: 0

Question Number 145759 Answers: 1 Comments: 2

Question Number 145756 Answers: 2 Comments: 0

Question Number 145809 Answers: 1 Comments: 0

prove 1+2+3+.....=−(1/(12))

$$\mathrm{prove}\:\mathrm{1}+\mathrm{2}+\mathrm{3}+.....=−\frac{\mathrm{1}}{\mathrm{12}} \\ $$

Question Number 145751 Answers: 1 Comments: 4

Question Number 145750 Answers: 0 Comments: 0

find Σ_(n=0) ^∞ (((−1)^n )/((2n+1)^3 (n+3)^2 ))

$$\mathrm{find}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{n}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 145749 Answers: 1 Comments: 0

g(x)=log(tan(x)) developp g at fourier serie

$$\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\left(\mathrm{tan}\left(\mathrm{x}\right)\right)\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Pg 715 Pg 716 Pg 717 Pg 718 Pg 719 Pg 720 Pg 721 Pg 722 Pg 723 Pg 724

Contact: info@tinkutara.com