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Question Number 199898 Answers: 1 Comments: 0

Question Number 199876 Answers: 0 Comments: 0

Question Number 199864 Answers: 1 Comments: 0

Find the remainder Σ_(n=1) ^(2019) n^4 when divide by 53

$$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{2019}} {\sum}}\mathrm{n}^{\mathrm{4}} \:\mathrm{when} \\ $$$$\:\:\mathrm{divide}\:\mathrm{by}\:\mathrm{53}\: \\ $$

Question Number 199863 Answers: 1 Comments: 0

−5+(−8)+(−11)+...+(−230)

$$−\mathrm{5}+\left(−\mathrm{8}\right)+\left(−\mathrm{11}\right)+...+\left(−\mathrm{230}\right) \\ $$

Question Number 199862 Answers: 0 Comments: 0

consider the taylor expansion of the function (1/(1+x^3 )) centered at x = 1/2 then the radius of convergence of the power series repersentation of the function is

$$\mathrm{consider}\:\mathrm{the}\:\mathrm{taylor}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{3}} } \\ $$$$\mathrm{centered}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{1}/\mathrm{2}\:\mathrm{then}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{convergence} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{power}\:\mathrm{series}\:\mathrm{repersentation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{is} \\ $$

Question Number 199858 Answers: 3 Comments: 0

Question Number 199893 Answers: 0 Comments: 2

Question Number 199891 Answers: 0 Comments: 1

solve by laplce transform y^(′′) −y^′ +y =(x+1)e^x

$${solve}\:{by}\:{laplce}\:{transform} \\ $$$${y}^{''} −{y}^{'} +{y}\:=\left({x}+\mathrm{1}\right){e}^{{x}} \\ $$

Question Number 199890 Answers: 0 Comments: 0

Question Number 199889 Answers: 0 Comments: 0

Question Number 199888 Answers: 0 Comments: 0

Question Number 199854 Answers: 1 Comments: 0

Question Number 199847 Answers: 0 Comments: 6

Find all possible value (a/(a+b+d )) +(b/(a+b+c)) + (c/(b+c+d))+(d/(a+c+d)) when a,b,c,d vary over positive reals

$$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{value}\: \\ $$$$\:\frac{\mathrm{a}}{\mathrm{a}+\mathrm{b}+\mathrm{d}\:}\:+\frac{\mathrm{b}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:+\:\frac{\mathrm{c}}{\mathrm{b}+\mathrm{c}+\mathrm{d}}+\frac{\mathrm{d}}{\mathrm{a}+\mathrm{c}+\mathrm{d}}\: \\ $$$$\:\mathrm{when}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{vary}\:\mathrm{over}\:\mathrm{positive} \\ $$$$\:\mathrm{reals}\: \\ $$

Question Number 199844 Answers: 2 Comments: 0

solve (d^2 /dx^2 ) x

$$\mathrm{solve}\:\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }\:\mathrm{x} \\ $$

Question Number 199840 Answers: 1 Comments: 0

Question Number 199838 Answers: 1 Comments: 0

Question Number 199837 Answers: 1 Comments: 0

Question Number 199836 Answers: 0 Comments: 3

Question Number 199843 Answers: 1 Comments: 0

lim_(x→0) ((1/(ln(1+x) ))−(1/(ln(x+(√(1+x^2 )) )))) = ??

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{1}+{x}\right)\:}−\frac{\mathrm{1}}{\mathrm{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\right)}\right)\:=\:?? \\ $$

Question Number 199834 Answers: 1 Comments: 1

Let C be the circle with the center (2,3) and radius 5 a) show that P(5,7) lies on C and find the equation of the tangent at P b) show that the line 3x−4y+31=0 is a tangent to C

$$\boldsymbol{{Let}}\:\boldsymbol{{C}}\:\boldsymbol{{be}}\:\boldsymbol{{the}}\:\boldsymbol{{circle}}\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{center}}\:\left(\mathrm{2},\mathrm{3}\right)\:\boldsymbol{{and}}\:\boldsymbol{{radius}}\:\mathrm{5} \\ $$$$\left.\boldsymbol{{a}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}\left(\mathrm{5},\mathrm{7}\right)\:\boldsymbol{{lies}}\:\boldsymbol{{on}}\:\boldsymbol{{C}}\:\boldsymbol{{and}}\:\boldsymbol{{find}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{equation}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{tangent}}\:\boldsymbol{{at}}\:\boldsymbol{{P}} \\ $$$$\left.\boldsymbol{{b}}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\mathrm{3}\boldsymbol{{x}}−\mathrm{4}\boldsymbol{{y}}+\mathrm{31}=\mathrm{0}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{tangent}}\:\boldsymbol{{to}}\:\boldsymbol{{C}} \\ $$

Question Number 199830 Answers: 1 Comments: 0

Si cos x+sin x=((1+(√3))/2) , halle el valor de la expresion R= 16(sin^6 x+cos^6 x)+3(sec^2 x+csc^2 x)

$$\:\:\mathrm{Si}\:\mathrm{cos}\:\mathrm{x}+\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{1}+\sqrt{\mathrm{3}}}{\mathrm{2}}\:, \\ $$$$\:\mathrm{halle}\:\mathrm{el}\:\mathrm{valor}\:\mathrm{de}\:\mathrm{la}\:\mathrm{expresion}\: \\ $$$$\:\mathrm{R}=\:\mathrm{16}\left(\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}\right)+\mathrm{3}\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{csc}^{\mathrm{2}} \:\mathrm{x}\right) \\ $$

Question Number 199821 Answers: 0 Comments: 2

ABFE Care determiner x en fonction de a etb BC=a DE= b

$$\mathrm{ABFE}\:\:\mathrm{Care} \\ $$$$\mathrm{determiner}\:\boldsymbol{\mathrm{x}}\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{a}\:\mathrm{etb} \\ $$$$\mathrm{BC}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\:\mathrm{DE}=\:\boldsymbol{\mathrm{b}} \\ $$

Question Number 199825 Answers: 1 Comments: 0

Question Number 199817 Answers: 2 Comments: 0

Question Number 199801 Answers: 1 Comments: 0

Question Number 199783 Answers: 1 Comments: 0

∫xdx=?

$$\int{xdx}=? \\ $$

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