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AllQuestion and Answers: Page 177

Question Number 204994 Answers: 2 Comments: 0

Question Number 204991 Answers: 2 Comments: 1

Question Number 204992 Answers: 1 Comments: 0

Is there any way to integrate: ∫ (1/( (√(ln(x))))) dx without hitting the Gauss error function or e^t^2 and e^(−t^2 ) ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{integrate}: \\ $$$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}\right)}}\:{dx} \\ $$$$\mathrm{without}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{error}\:\mathrm{function} \\ $$$$\mathrm{or}\:{e}^{{t}^{\mathrm{2}} } \:\mathrm{and}\:{e}^{−{t}^{\mathrm{2}} } \:? \\ $$

Question Number 204985 Answers: 1 Comments: 0

Q=∫_0 ^1 (((1−x^3 )(1−x^(33) )(1−x^(333) ))/(lnx))dx

$${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\left(\mathrm{1}−{x}^{\mathrm{33}} \right)\left(\mathrm{1}−{x}^{\mathrm{333}} \right)}{{lnx}}{dx} \\ $$

Question Number 204979 Answers: 4 Comments: 0

factorizar x^4 + 1

$${factorizar} \\ $$$${x}^{\mathrm{4}} \:+\:\mathrm{1} \\ $$

Question Number 204978 Answers: 1 Comments: 0

Question Number 204970 Answers: 1 Comments: 1

Question Number 204961 Answers: 2 Comments: 0

∫ (1/(1+cot 3x)) dx =

$$\int\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:\mathrm{3}{x}}\:{dx}\:=\:\: \\ $$

Question Number 204957 Answers: 2 Comments: 0

2×2 matrix A and B satisfy that AB+A=BA+B. Prove that (A−B)^2 =O.

$$\mathrm{2}×\mathrm{2}\:\mathrm{matrix}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{satisfy}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{AB}}+\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{BA}}+\boldsymbol{\mathrm{B}}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right)^{\mathrm{2}} =\boldsymbol{\mathrm{O}}. \\ $$

Question Number 204948 Answers: 0 Comments: 4

prove a^2 +b^2 +c^2 +((abc))^(1/3) ≥4 if ab+bc+ac=3

$${prove}\: \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\sqrt[{\mathrm{3}}]{{abc}}\geqslant\mathrm{4} \\ $$$${if} \\ $$$${ab}+{bc}+{ac}=\mathrm{3} \\ $$

Question Number 204947 Answers: 1 Comments: 0

f′(x)+4x−6x.e^(x^2 −f(x)−1) =0 f(x)=¿

$${f}'\left({x}\right)+\mathrm{4}{x}−\mathrm{6}{x}.{e}^{{x}^{\mathrm{2}} −{f}\left({x}\right)−\mathrm{1}} =\mathrm{0} \\ $$$${f}\left({x}\right)=¿ \\ $$

Question Number 204944 Answers: 1 Comments: 1

Question Number 204941 Answers: 0 Comments: 0

Question Number 205204 Answers: 1 Comments: 0

Question Number 204929 Answers: 1 Comments: 0

lim_(n→∞) Π_(r=1) ^n ((n^2 −r)/(n^2 +r)) = ?

$$\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\prod}}\:\frac{{n}^{\mathrm{2}} −{r}}{{n}^{\mathrm{2}} +{r}}\:\:=\:\:? \\ $$

Question Number 204926 Answers: 0 Comments: 2

Prove that in any △ABC (m_a + m_b + m_c )^2 ≥ 9(√3) F

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\mathrm{any}\:\bigtriangleup\mathrm{ABC} \\ $$$$\left(\mathrm{m}_{\boldsymbol{\mathrm{a}}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{b}}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{c}}} \right)^{\mathrm{2}} \:\geqslant\:\mathrm{9}\sqrt{\mathrm{3}}\:\mathrm{F} \\ $$

Question Number 204921 Answers: 1 Comments: 0

Question Number 204920 Answers: 1 Comments: 0

16^(y+x^2 ) + 16^(y^2 +x) = 1 x+y =?

$$\:\:\:\:\:\mathrm{16}^{\mathrm{y}+\mathrm{x}^{\mathrm{2}} } \:+\:\mathrm{16}^{\mathrm{y}^{\mathrm{2}} +\mathrm{x}} \:=\:\mathrm{1}\: \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{y}\:=? \\ $$

Question Number 204916 Answers: 0 Comments: 8

How many axes of symmetry does an open angle have?

$$ \\ $$How many axes of symmetry does an open angle have?

Question Number 204910 Answers: 1 Comments: 1

Question Number 204909 Answers: 1 Comments: 0

Ω= ∫_(1/e) ^( e) (( arctan(x))/x) dx=?

$$ \\ $$$$\:\:\:\:\:\:\:\Omega=\:\int_{\frac{\mathrm{1}}{{e}}} ^{\:{e}} \frac{\:{arctan}\left({x}\right)}{{x}}\:{dx}=? \\ $$

Question Number 204902 Answers: 2 Comments: 0

calculate ∫_0 ^1 (√(x(1−x)))dx

$$\boldsymbol{{calculate}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}\boldsymbol{{dx}} \\ $$

Question Number 204901 Answers: 0 Comments: 0

Question Number 204900 Answers: 0 Comments: 2

lim_(n→∞) n!(e−x_n ) = ? where x_(n ) = 1+(1/(1!))+(1/(2!))+...+(1/(n!))

$$\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}!\left({e}−\mathrm{x}_{\mathrm{n}} \right)\:=\:? \\ $$$$\:\:\mathrm{where}\:\mathrm{x}_{\mathrm{n}\:} =\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}+...+\frac{\mathrm{1}}{\mathrm{n}!} \\ $$

Question Number 204890 Answers: 2 Comments: 1

Question Number 204885 Answers: 1 Comments: 0

The density of a gas is 1.775kgm³ at 29°c and 10⁵N/m² pressure, its specific heat capacity at constant pressure is 856J/kg/K. Determine the ratio of its specific heat at constant pressure to that at constant volume?

Pg 172 Pg 173 Pg 174 Pg 175 Pg 176 Pg 177 Pg 178 Pg 179 Pg 180 Pg 181

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