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Question Number 208900 Answers: 0 Comments: 0

Does anyone know of an intuition behind the integral form of the remainder in Taylor′s theorem?

$${Does}\:{anyone}\:{know}\:{of}\:{an}\:{intuition} \\ $$$${behind}\:{the}\:{integral}\:{form}\:{of}\:{the} \\ $$$${remainder}\:{in}\:{Taylor}'{s}\:{theorem}? \\ $$

Question Number 208915 Answers: 1 Comments: 0

Question Number 208896 Answers: 2 Comments: 0

Question Number 208891 Answers: 0 Comments: 0

$$\:\:\:\underline{\kappa} \\ $$

Question Number 208892 Answers: 2 Comments: 1

Find: (√(−16)) ∙ (√(−9)) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{−\mathrm{16}}\:\:\centerdot\:\:\sqrt{−\mathrm{9}}\:\:=\:\:? \\ $$

Question Number 208880 Answers: 1 Comments: 0

Question Number 208876 Answers: 2 Comments: 7

The 𝚌a𝚕𝚎𝚗𝚍𝚊𝚛 𝚘𝚏 𝚝𝚑𝚎 𝚢𝚎𝚊𝚛 2024 𝚒𝚜 𝚝𝚑𝚎 𝚜𝚊𝚖𝚎 𝚏𝚘𝚛 𝙰.2044 𝙱.2032 𝙲.2040 𝙳.2036

Question Number 208872 Answers: 2 Comments: 0

Find the side of a triangle if the distances from an arbitrary point inside a regular triangle to its vertices are m, n and k. Help please

$$ \\ $$$$\:\:\:{Find}\:{the}\:{side}\:{of}\:{a}\:{triangle}\:{if}\:{the}\:{distances} \\ $$$$\:\:\:{from}\:{an}\:{arbitrary}\:{point}\:{inside}\:{a}\:{regular}\:{triangle}\: \\ $$$$\:\:\:{to}\:{its}\:{vertices}\:{are}\:{m},\:{n}\:{and}\:{k}. \\ $$$$\:\:{Help}\:{please} \\ $$

Question Number 208871 Answers: 3 Comments: 0

L=∫_0 ^1 (√((4−3x)/(4+5x)))dx

$${L}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}{dx} \\ $$

Question Number 208866 Answers: 1 Comments: 1

Question Number 208861 Answers: 0 Comments: 2

Question Number 208855 Answers: 1 Comments: 0

Question Number 208852 Answers: 1 Comments: 0

Question Number 208849 Answers: 0 Comments: 0

Question Number 208842 Answers: 1 Comments: 1

does the rule of odd and even functions can be applied with improper integration? I=∫_(−∞) ^∞ xe^(−x^2 ) dx while f(x)= xe^(−x^2 ) is odd then I =0

$${does}\:{the}\:{rule}\:{of}\:{odd}\:{and}\:{even}\:{functions}\: \\ $$$${can}\:{be}\:{applied}\:{with}\:{improper}\:{integration}? \\ $$$${I}=\int_{−\infty} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {dx}\: \\ $$$${while}\:\:{f}\left({x}\right)=\:{xe}^{−{x}^{\mathrm{2}} } \:{is}\:{odd} \\ $$$${then}\:{I}\:=\mathrm{0} \\ $$

Question Number 208836 Answers: 2 Comments: 0

Question Number 208828 Answers: 3 Comments: 0

Question Number 208823 Answers: 2 Comments: 0

If a+b+c=15, then find the smallest value of the expression (√(a^2 +1))+(√(b^2 +9))+(√(c^2 +16)). Help please

$$ \\ $$$$\:\:\:{If}\:{a}+{b}+{c}=\mathrm{15},\:{then}\:{find}\:{the}\:{smallest}\:{value}\: \\ $$$$\:\:\:{of}\:{the}\:{expression}\:\sqrt{{a}^{\mathrm{2}} +\mathrm{1}}+\sqrt{{b}^{\mathrm{2}} +\mathrm{9}}+\sqrt{{c}^{\mathrm{2}} +\mathrm{16}}. \\ $$$$\:\:\:\:\:{Help}\:{please} \\ $$

Question Number 208819 Answers: 2 Comments: 0

Question Number 208816 Answers: 0 Comments: 1

Question Number 208814 Answers: 1 Comments: 2

Question Number 208809 Answers: 0 Comments: 1

Question Number 208812 Answers: 1 Comments: 0

Question Number 208805 Answers: 0 Comments: 3

Integrate: (xdz − zdx) − a^2 (2xzdz − z^2 dx) + 2x^3 = 0

$$\mathrm{Integrate}: \\ $$$$\left(\mathrm{xdz}\:−\:\mathrm{zdx}\right)\:−\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{2xzdz}\:−\:\mathrm{z}^{\mathrm{2}} \mathrm{dx}\right)\:+\:\mathrm{2x}^{\mathrm{3}} \:=\:\mathrm{0} \\ $$

Question Number 208791 Answers: 0 Comments: 1

If ∫ (dx/(x^3 (1 + x^6 )^(2/3) )) = xf(x).(1 + x^6 )^(1/3) + C where C is constant of integration then find f(x).

$$\mathrm{If}\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:=\:{xf}\left({x}\right).\left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:{C}\: \\ $$$$\mathrm{where}\:{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{then} \\ $$$$\mathrm{find}\:{f}\left({x}\right). \\ $$

Question Number 208789 Answers: 0 Comments: 3

Why is surface tension formula divided by 2L that is, surface tension = (F/(2L)) why divided by 2L. Where did the 2 come from? Example. Calculate the force required to lift a needle 4cm long off the surface of water, if surface tension of water is 7.3 × 10^(−4) Nm^(− 1) Why is the formula surface tension = (F/(2L)) why not surface tension = (F/L)

$$\mathrm{Why}\:\mathrm{is}\:\mathrm{surface}\:\mathrm{tension}\:\mathrm{formula}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L} \\ $$$$\mathrm{that}\:\mathrm{is},\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L}. \\ $$$$\mathrm{Where}\:\mathrm{did}\:\mathrm{the}\:\mathrm{2}\:\mathrm{come}\:\mathrm{from}? \\ $$$$ \\ $$$$\mathrm{Example}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{force}\:\mathrm{required}\:\mathrm{to}\:\mathrm{lift}\:\mathrm{a}\:\mathrm{needle} \\ $$$$\mathrm{4cm}\:\mathrm{long}\:\mathrm{off}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{water},\:\mathrm{if}\:\mathrm{surface} \\ $$$$\mathrm{tension}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{−\mathrm{4}} \mathrm{Nm}^{−\:\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{the}\:\mathrm{formula}\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{not}\:\:\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{L}} \\ $$

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