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Question Number 112494 Answers: 2 Comments: 0

y(√(1+x^2 )) dx + x(√(1+y^2 )) dy = 0

$$\:\mathrm{y}\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:+\:\mathrm{x}\sqrt{\mathrm{1}+\mathrm{y}^{\mathrm{2}} }\:\mathrm{dy}\:=\:\mathrm{0} \\ $$

Question Number 112492 Answers: 1 Comments: 0

evaluate lim_(n→∞) Σ_(k=1) ^n (1/(n+k^2 ))

$${evaluate} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}^{\mathrm{2}} } \\ $$

Question Number 112498 Answers: 0 Comments: 0

∫((ln(1+x)dx)/((1+x^2 )))

$$\int\frac{{ln}\left(\mathrm{1}+{x}\right){dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)} \\ $$

Question Number 112497 Answers: 2 Comments: 0

If lim_(x→0) ((sin 2x + asin x)/x^3 ) exist what is the value of a and the limit?

$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{asin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:\mathrm{exist}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{the}\:\mathrm{limit}? \\ $$

Question Number 112481 Answers: 1 Comments: 0

∫ ((sin 2x)/( (√(1+cos^2 x)))) dx

$$\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}}\:\mathrm{dx}\: \\ $$

Question Number 112478 Answers: 1 Comments: 0

If P(x)= x^3 +ax^2 +bx+c, with a, b and c real numbers. Roots of P(x) z+3i, z+9i and 2z−4, find ∣a+b+c∣. Note: z is complex number.

$${If}\:{P}\left({x}\right)=\:{x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c},\:{with}\:{a},\:{b}\:{and}\:{c}\:{real}\:{numbers}. \\ $$$${Roots}\:{of}\:{P}\left({x}\right)\:{z}+\mathrm{3}{i},\:{z}+\mathrm{9}{i}\:{and}\:\mathrm{2}{z}−\mathrm{4},\:{find}\:\mid{a}+{b}+{c}\mid. \\ $$$$\boldsymbol{{N}}{ote}:\:{z}\:{is}\:{complex}\:{number}. \\ $$

Question Number 112467 Answers: 1 Comments: 0

Question Number 112466 Answers: 1 Comments: 0

Question Number 112465 Answers: 1 Comments: 0

Question Number 112464 Answers: 1 Comments: 0

Question Number 112461 Answers: 1 Comments: 0

If x, y and z are numbers integers different of 0 { ((49x+7y+z=0)),((25x−5y+z=0)) :} find (√(y^2 −4xz))

$${If}\:\:\:{x},\:{y}\:{and}\:{z}\:\:{are}\:{numbers}\:\:{integers}\:{different}\:{of}\:\:\:\mathrm{0} \\ $$$$\begin{cases}{\mathrm{49}{x}+\mathrm{7}{y}+{z}=\mathrm{0}}\\{\mathrm{25}{x}−\mathrm{5}{y}+{z}=\mathrm{0}}\end{cases}\:\:\:\:\:\:\:\:\:{find}\:\sqrt{{y}^{\mathrm{2}} −\mathrm{4}{xz}} \\ $$

Question Number 112456 Answers: 3 Comments: 0

solve (dy/dx)−((4y)/x) = 1+(2/x)

$$\mathrm{solve}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\frac{\mathrm{4y}}{\mathrm{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}} \\ $$

Question Number 112455 Answers: 2 Comments: 0

(1)lim_(x→p) ((p^x −x^p )/(x^x −p^p )) ? (2) There are 4 identical math books, 2 identical physics books and 2 identical chemistry books. How many ways to compile the eight books on the condition of the same books are not mutually adjacent?

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mathrm{p}^{\mathrm{x}} −\mathrm{x}^{\mathrm{p}} }{\mathrm{x}^{\mathrm{x}} −\mathrm{p}^{\mathrm{p}} }\:?\: \\ $$$$\left(\mathrm{2}\right)\:{There}\:{are}\:\mathrm{4}\:{identical}\:{math}\:{books}, \\ $$$$\mathrm{2}\:{identical}\:{physics}\:{books}\:{and}\:\mathrm{2}\:{identical} \\ $$$${chemistry}\:{books}.\:{How}\:{many}\:{ways}\:{to} \\ $$$${compile}\:{the}\:{eight}\:{books}\:{on}\:{the}\: \\ $$$${condition}\:{of}\:{the}\:{same}\:{books}\:{are}\:{not} \\ $$$${mutually}\:{adjacent}? \\ $$

Question Number 112454 Answers: 1 Comments: 1

(1) find the locus ∣z−z_1 ∣ = 2 meets the positive real axis (2)On a single Argand diagram, sketch the loci → { ((∣z−z_1 ∣=2)),((arg(z−z_2 )=(π/4))) :}

$$\left(\mathrm{1}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{locus}\:\mid\mathrm{z}−\mathrm{z}_{\mathrm{1}} \mid\:=\:\mathrm{2}\:\mathrm{meets} \\ $$$$\mathrm{the}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{axis} \\ $$$$\left(\mathrm{2}\right)\mathrm{On}\:\mathrm{a}\:\mathrm{single}\:\mathrm{Argand}\:\mathrm{diagram},\:\mathrm{sketch} \\ $$$$\mathrm{the}\:\mathrm{loci}\:\rightarrow\begin{cases}{\mid\mathrm{z}−\mathrm{z}_{\mathrm{1}} \mid=\mathrm{2}}\\{\mathrm{arg}\left(\mathrm{z}−\mathrm{z}_{\mathrm{2}} \right)=\frac{\pi}{\mathrm{4}}}\end{cases} \\ $$

Question Number 112447 Answers: 0 Comments: 0

calculate ∫_0 ^1 ((ln(1+x^2 ))/(1+x^3 )) dx

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

Question Number 112446 Answers: 2 Comments: 0

find ∫_0 ^1 ((ln(1+x^2 ))/(1+x))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}+\mathrm{x}}\mathrm{dx} \\ $$

Question Number 112449 Answers: 3 Comments: 3

1)calculste A=∫_(−∞) ^(+∞) (dx/((x^2 −ix +1)^2 )) 2) extract Re(A) and Im(A) and determines its values

$$\left.\mathrm{1}\right)\mathrm{calculste}\:\:\mathrm{A}=\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{ix}\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{extract}\:\mathrm{Re}\left(\mathrm{A}\right)\:\mathrm{and}\:\mathrm{Im}\left(\mathrm{A}\right)\:\mathrm{and}\:\mathrm{determines}\:\mathrm{its}\:\mathrm{values} \\ $$

Question Number 112430 Answers: 0 Comments: 0

Π_(n=1) ^∞ (1/(1−x^n ))