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AllQuestion and Answers: Page 1226

Question Number 86657 Answers: 1 Comments: 0

solve (1+x^3 )dy −x^2 y dx=0 y(1) = 2

$$\mathrm{solve}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)\mathrm{dy}\:−\mathrm{x}^{\mathrm{2}} \:\mathrm{y}\:\mathrm{dx}=\mathrm{0} \\ $$$$\mathrm{y}\left(\mathrm{1}\right)\:=\:\mathrm{2} \\ $$

Question Number 86655 Answers: 1 Comments: 0

lim_(x→−1^+ ) (((√π) −(√(arc cos x)))/(√(x+1)))

$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\pi}\:−\sqrt{\mathrm{arc}\:\mathrm{cos}\:\mathrm{x}}}{\sqrt{\mathrm{x}+\mathrm{1}}} \\ $$

Question Number 86646 Answers: 0 Comments: 2

∫_0 ^1 ((ln(1+x))/(x^2 +1))dx

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

Question Number 86643 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((cos(2ch(x)))/(x^2 +9))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{ch}\left({x}\right)\right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 86640 Answers: 1 Comments: 0

Solve the differential equations: (i).x^2 (d^2 y/dx^2 ) − x(dy/dx) + y = log x. (ii). (x+2)^2 (d^2 y/dx^2 ) − 4(x+2)(dy/dx) + 6y = x.

Question Number 86638 Answers: 1 Comments: 0

I=∫((x^3 −2x^2 +7x−1)/((x−3)^3 (x−2)^2 ))dx

$${I}=\int\frac{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{1}}{\left({x}−\mathrm{3}\right)^{\mathrm{3}} \left({x}−\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 86634 Answers: 1 Comments: 0

Question Number 86627 Answers: 1 Comments: 3

Question Number 86626 Answers: 1 Comments: 2

∫(√(x^2 +4)) dx answer quick pls

$$\int\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\:\:\mathrm{dx} \\ $$$$\mathrm{answer}\:\mathrm{quick}\:\mathrm{pls} \\ $$

Question Number 86615 Answers: 1 Comments: 2

∫(√(tan x ))dx

$$\int\sqrt{{tan}\:{x}\:}{dx} \\ $$

Question Number 86614 Answers: 1 Comments: 0

ABC is an isocel triangle such as AB=AC=3 and BC=4 α , β , and γ are its angles. Show that cos(((α+β)/2))=sin((γ/2)) Hi sirs...

$${ABC}\:{is}\:{an}\:{isocel}\:{triangle}\:{such}\:{as} \\ $$$${AB}={AC}=\mathrm{3}\:\:{and}\:{BC}=\mathrm{4} \\ $$$$\alpha\:,\:\beta\:,\:{and}\:\gamma\:{are}\:{its}\:{angles}. \\ $$$${Show}\:{that}\:{cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right)={sin}\left(\frac{\gamma}{\mathrm{2}}\right) \\ $$$${Hi}\:{sirs}... \\ $$

Question Number 86613 Answers: 0 Comments: 6

∫_0 ^(1/2) ∫_0 ^(π/2) (1/(ycos(x)+1))dxdy

$$\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{{ycos}\left({x}\right)+\mathrm{1}}{dxdy} \\ $$$$ \\ $$

Question Number 86611 Answers: 1 Comments: 0

∫_1 ^e ((ln x)/(x+1))dx

$$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 86610 Answers: 0 Comments: 4

Question Number 86603 Answers: 2 Comments: 2

lim_(x→−1) (e^x /((1+x)^n ))

$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\frac{{e}^{{x}} }{\left(\mathrm{1}+{x}\right)^{{n}} } \\ $$

Question Number 86602 Answers: 0 Comments: 0

Question Number 86598 Answers: 0 Comments: 1

write out the general summation formula for the maclaurin series expansion for (1/2) (cos x + cosh x)

$$\:\mathrm{write}\:\mathrm{out}\:\mathrm{the}\:\mathrm{general}\:\mathrm{summation}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\:\mathrm{the}\:\mathrm{maclaurin}\:\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{cos}\:{x}\:+\:\mathrm{cosh}\:{x}\right) \\ $$

Question Number 86592 Answers: 0 Comments: 1

prove that 2Σ_(x=1) ^∞ ((2^x (x!)^2 )/((2x)! (x)))

$${prove}\:{that} \\ $$$$\mathrm{2}\underset{{x}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{{x}} \:\left({x}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{x}\right)!\:\left({x}\right)} \\ $$

Question Number 86591 Answers: 0 Comments: 0

∫_(−1) ^1 ⌊ ∣x∣+(x)^(1/3) ⌋ dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \lfloor\:\mid{x}\mid+\sqrt[{\mathrm{3}}]{{x}}\:\rfloor\:{dx} \\ $$

Question Number 86586 Answers: 1 Comments: 4

Question Number 86578 Answers: 0 Comments: 2

Question Number 86576 Answers: 0 Comments: 3

∫ ((ln (1+arc sin (x^2 )))/(sin (x^2 ))) dx ?

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

Question Number 86560 Answers: 0 Comments: 4

x = 1 + (3/4) + ((15)/(32)) + ((105)/(384)) + ... x^2 − 1 = ?

$${x}\:\:=\:\:\mathrm{1}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{15}}{\mathrm{32}}\:+\:\frac{\mathrm{105}}{\mathrm{384}}\:+\:... \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{1}\:\:=\:\:? \\ $$

Question Number 86558 Answers: 0 Comments: 0

For any integer n,∫_( 0) ^π e^(cos^2 x) cos^3 (2n+1)x dx=

$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\underset{\:\mathrm{0}} {\overset{\pi} {\int}}{e}^{\mathrm{cos}^{\mathrm{2}} {x}} \mathrm{cos}^{\mathrm{3}} \left(\mathrm{2}{n}+\mathrm{1}\right){x}\:{dx}= \\ $$

Question Number 86552 Answers: 0 Comments: 3

proe that f(x)=x+[x] increase in R

$${proe}\:{that} \\ $$$${f}\left({x}\right)={x}+\left[{x}\right]\: \\ $$$${increase}\:{in}\:{R} \\ $$

Question Number 86550 Answers: 1 Comments: 3

show that tan^(−1) x=((ln (−x^2 +2ix+1)−ln (x^2 +1))/(2i))

$$\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}\:^{−\mathrm{1}} {x}=\frac{\mathrm{ln}\:\left(−{x}^{\mathrm{2}} +\mathrm{2}{ix}+\mathrm{1}\right)−\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{2}{i}} \\ $$

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