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Question Number 77856 Answers: 1 Comments: 1

l_(x→0) im(((e^x −x−1)/x))

$$\underset{{x}\rightarrow\mathrm{0}} {{l}im}\left(\frac{{e}^{{x}} −{x}−\mathrm{1}}{{x}}\right) \\ $$

Question Number 77855 Answers: 0 Comments: 0

Question Number 77854 Answers: 1 Comments: 1

a circle offends the y axis at point(0,b) and through the intersection of the curve y = x −2(√x)+(1/4). value of b = ?

$${a}\:{circle}\: \\ $$$${offends}\:{the}\:{y}\:{axis}\:{at}\:{point}\left(\mathrm{0},{b}\right)\: \\ $$$${and}\:{through}\:{the}\:{intersection} \\ $$$${of}\:{the}\:{curve}\:{y}\:=\:{x}\:−\mathrm{2}\sqrt{{x}}+\frac{\mathrm{1}}{\mathrm{4}}.\: \\ $$$${value}\:{of}\:{b}\:=\:? \\ $$

Question Number 77852 Answers: 0 Comments: 0

5245

$$\mathrm{5245} \\ $$

Question Number 77848 Answers: 0 Comments: 3

Question Number 77845 Answers: 0 Comments: 0

In the equation B=μ_0 H×μ_0 M why is the polarization of the vacuum accounted for by constant μ_0 if the vacuum is absolutely empty?

$$\boldsymbol{\mathrm{I}}\mathrm{n}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\boldsymbol{\mathrm{B}}=\mu_{\mathrm{0}} \boldsymbol{\mathrm{H}}×\mu_{\mathrm{0}} \boldsymbol{\mathrm{M}}\: \\ $$$$\mathrm{why}\:\mathrm{is}\:\mathrm{the}\:\mathrm{polarization}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vacuum}\: \\ $$$$\mathrm{accounted}\:\mathrm{for}\:\mathrm{by}\: \\ $$$$\mathrm{constant}\:\mu_{\mathrm{0}} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{vacuum}\:\mathrm{is}\:\mathrm{absolutely}\:\mathrm{empty}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 77842 Answers: 1 Comments: 0

given f(x)= x^2 +sin(2x) + ∫ _0 ^(π/4) f(x)dx f((π/2))=?

$${given}\: \\ $$$${f}\left({x}\right)=\:{x}^{\mathrm{2}} +\mathrm{sin}\left(\mathrm{2}{x}\right)\:+\:\int\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\:}}{f}\left({x}\right){dx} \\ $$$${f}\left(\frac{\pi}{\mathrm{2}}\right)=? \\ $$

Question Number 77838 Answers: 0 Comments: 0

anyone know link the Latex for phone?

$${anyone}\:{know} \\ $$$${link}\:{the}\:{Latex}\:{for}\:{phone}? \\ $$

Question Number 77819 Answers: 2 Comments: 0

Question Number 77817 Answers: 0 Comments: 3

∫(dx/(x^3 (x^2 +2x+5)^4 ))

$$\int\frac{{dx}}{{x}^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}\right)^{\mathrm{4}} } \\ $$$$ \\ $$

Question Number 77816 Answers: 0 Comments: 0

∫sin(x^2 ) sin(x) dx

$$\int{sin}\left({x}^{\mathrm{2}} \right)\:{sin}\left({x}\right)\:{dx} \\ $$

Question Number 77813 Answers: 0 Comments: 0

What is a way to approximate some large number such as: Speed of light and Avogadro constant instead of write the whole number

$$\mathrm{What}\:\mathrm{is}\:\mathrm{a}\:\mathrm{way}\:\mathrm{to}\:\mathrm{approximate} \\ $$$$\mathrm{some}\:\mathrm{large}\:\mathrm{number}\:\mathrm{such}\:\mathrm{as}: \\ $$$$\mathrm{Speed}\:\mathrm{of}\:\mathrm{light}\:\mathrm{and}\:\mathrm{Avogadro} \\ $$$$\mathrm{constant}\:\mathrm{instead}\:\mathrm{of}\:\mathrm{write}\:\mathrm{the} \\ $$$$\mathrm{whole}\:\mathrm{number} \\ $$

Question Number 77810 Answers: 2 Comments: 0

what is minimum value of function f(x)= (√(x^2 +4)) +(√(x^2 −24x+153))

$${what}\:{is}\:{minimum}\:{value} \\ $$$${of}\:{function}\:{f}\left({x}\right)= \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\sqrt{{x}^{\mathrm{2}} −\mathrm{24}{x}+\mathrm{153}} \\ $$

Question Number 77805 Answers: 1 Comments: 0

Solve for x ((8^x + 27^x )/(12^x + 18^x )) = (7/6)

$${Solve}\:{for}\:{x} \\ $$$$\frac{\mathrm{8}^{{x}} \:+\:\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} \:+\:\mathrm{18}^{{x}} }\:=\:\frac{\mathrm{7}}{\mathrm{6}} \\ $$

Question Number 77804 Answers: 0 Comments: 2

Question Number 77803 Answers: 1 Comments: 0

solve (4x^2 +4x+1)y′′−(12x+6)y′−8x^3 −1=12x^2 −16y+6x

$${solve} \\ $$$$\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}\right){y}''−\left(\mathrm{12}{x}+\mathrm{6}\right){y}'−\mathrm{8}{x}^{\mathrm{3}} −\mathrm{1}=\mathrm{12}{x}^{\mathrm{2}} −\mathrm{16}{y}+\mathrm{6}{x} \\ $$

Question Number 77802 Answers: 0 Comments: 0

Question Number 77800 Answers: 0 Comments: 0

if a_1 =1, a_2 =3 and a_n =(√(a_(n−1) +a_(n−2) )) with n≥3 find a_n in explicit form.

$${if}\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} }\:{with}\:{n}\geqslant\mathrm{3} \\ $$$${find}\:{a}_{{n}} \:{in}\:{explicit}\:{form}. \\ $$

Question Number 77799 Answers: 1 Comments: 0

if a_1 =3 and a_(n+1) =3a_n +6n^2 −12n+2 find a_n in terms of n.

$${if}\:{a}_{\mathrm{1}} =\mathrm{3}\:{and} \\ $$$${a}_{{n}+\mathrm{1}} =\mathrm{3}{a}_{{n}} +\mathrm{6}{n}^{\mathrm{2}} −\mathrm{12}{n}+\mathrm{2} \\ $$$${find}\:{a}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$

Question Number 77790 Answers: 1 Comments: 0

∫_0 ^1 (1/(√(−log(x)))) dx

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

Question Number 77778 Answers: 0 Comments: 2

∫((cosx)/(2−cosx))dx

$$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx} \\ $$$$ \\ $$

Question Number 77777 Answers: 1 Comments: 0

The number of words can be made formed using all letters in the word ′amutasia′ by not containing the three vowels side by side is ?

$${The}\:{number} \\ $$$${of}\:{words}\:{can}\:{be}\:{made}\:{formed} \\ $$$${using}\:{all}\:{letters}\:{in}\:{the}\:{word} \\ $$$$'{amutasia}'\:{by}\:{not}\:{containing} \\ $$$${the}\:{three}\:{vowels}\:{side}\:{by}\:{side}\:{is}\:? \\ $$

Question Number 77765 Answers: 0 Comments: 2

Hello please how can we calculate the yield in % of ohmic conductor in actif circuit with Battery( with his resistance) and a motor( with his resistance) knowing theirs caracteristics and the intensity? I need a formula.

$$\mathrm{Hello}\: \\ $$$$\mathrm{please}\:\mathrm{how}\:\mathrm{can}\:\mathrm{we}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{yield} \\ $$$$\mathrm{in}\:\%\:\mathrm{of}\:\mathrm{ohmic}\:\mathrm{conductor}\:\mathrm{in}\:\mathrm{actif}\:\mathrm{circuit}\: \\ $$$$\mathrm{with}\:\mathrm{Battery}\left(\:\mathrm{with}\:\mathrm{his}\:\mathrm{resistance}\right) \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{motor}\left(\:\mathrm{with}\:\mathrm{his}\:\mathrm{resistance}\right) \\ $$$$\mathrm{knowing}\:\:\mathrm{theirs}\:\mathrm{caracteristics}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{intensity}? \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{a}\:\mathrm{formula}. \\ $$

Question Number 77760 Answers: 0 Comments: 0

find the value of Σ_(n=0) ^∞ (1/(n^2 +n+1))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}} \\ $$

Question Number 77759 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ (1/(n^2 +1))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 77758 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((√(3+x^2 ))/((x^2 +1)(√(x^2 −x+2))))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{\mathrm{3}+{x}^{\mathrm{2}} }}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{2}}}{dx} \\ $$

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