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Question Number 166617 Answers: 2 Comments: 1

Question Number 166616 Answers: 0 Comments: 0

calculate::lim_(n→∞) ((∣cos 1^2 ∣+cos ∣2^2 ∣+∣cos 3^2 ∣+...+∣cos n^2 ∣)/n)=(2/π)

$$\mathrm{calculate}::\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mid\mathrm{cos}\:\mathrm{1}^{\mathrm{2}} \mid+\mathrm{cos}\:\mid\mathrm{2}^{\mathrm{2}} \mid+\mid\mathrm{cos}\:\mathrm{3}^{\mathrm{2}} \mid+...+\mid\mathrm{cos}\:\mathrm{n}^{\mathrm{2}} \mid}{\mathrm{n}}=\frac{\mathrm{2}}{\pi} \\ $$

Question Number 166614 Answers: 0 Comments: 0

calculate:: ∫_0 ^∞ (({x}^2 (1−{x})^2 )/((1+x)^5 ))=(7/(12))−γ

$$\mathrm{calculate}::\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left\{\mathrm{x}\right\}^{\mathrm{2}} \left(\mathrm{1}−\left\{\mathrm{x}\right\}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{5}} }=\frac{\mathrm{7}}{\mathrm{12}}−\gamma \\ $$

Question Number 166612 Answers: 1 Comments: 2

∫_0 ^( (π/2)) (1/(1+cos(x)+2sin(x)))dx=?

$$ \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{1}+{cos}\left({x}\right)+\mathrm{2}{sin}\left({x}\right)}{dx}=? \\ $$

Question Number 166606 Answers: 0 Comments: 0

Question Number 166611 Answers: 0 Comments: 0

Given f(x) is a polynom give the remainder x^2 −x−1 when divided by x^4 +4. Find the remainder when f(x) divided by x^2 −2x+2.

$$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynom}\:\mathrm{give}\:\mathrm{the}\: \\ $$$$\:\mathrm{remainder}\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\: \\ $$$$\:\mathrm{x}^{\mathrm{4}} +\mathrm{4}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}. \\ $$

Question Number 166610 Answers: 1 Comments: 1

∫ ((x^2 +3)/(x^4 +5x^2 +9)) dx ?

$$\:\:\:\:\int\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}{\mathrm{x}^{\mathrm{4}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{9}}\:\mathrm{dx}\:? \\ $$

Question Number 166602 Answers: 0 Comments: 0

Determine condition/s that a number divisible by 11 is a palindrome-number.

$$\mathcal{D}{etermine}\:{condition}/{s}\:{that} \\ $$$${a}\:\boldsymbol{{number}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11} \\ $$$${is}\:{a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}}. \\ $$

Question Number 166601 Answers: 0 Comments: 0

What is the condition that a palindrome-number is divisible by 11?

$${What}\:{is}\:{the}\:{condition}\:{that}\: \\ $$$${a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}} \\ $$$$\:{is}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11}? \\ $$

Question Number 166597 Answers: 0 Comments: 0

Question Number 166596 Answers: 0 Comments: 0

Question Number 166592 Answers: 1 Comments: 0

Question Number 166585 Answers: 1 Comments: 0

if y = (sinx)^e^x find ((d ( e^(sin^(−1) y) ))/(d (lnx)))

$${if}\:{y}\:=\:\left({sinx}\right)^{{e}^{{x}} } \:{find}\:\frac{{d}\:\left(\:{e}^{{sin}^{−\mathrm{1}} {y}} \right)}{{d}\:\left({lnx}\right)} \\ $$

Question Number 166584 Answers: 1 Comments: 1

Question Number 166583 Answers: 1 Comments: 0

Question Number 166580 Answers: 1 Comments: 0

Question Number 166573 Answers: 1 Comments: 1

Question Number 166572 Answers: 2 Comments: 0

lim_(n→∞) Σ_(k=0) ^(2n) 2^(−k) cos (√(k/n))=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{2n}} {\sum}}\mathrm{2}^{−\mathrm{k}} \mathrm{cos}\:\sqrt{\frac{\mathrm{k}}{\mathrm{n}}}=? \\ $$

Question Number 166570 Answers: 1 Comments: 0

Question Number 166569 Answers: 0 Comments: 0

Question Number 166555 Answers: 0 Comments: 0

Question Number 166554 Answers: 0 Comments: 0

∫_(−∞) ^∞ sin ((1/2)πx(x+1)) cos (πx^2 ) dx=?

$$\:\:\:\int_{−\infty} ^{\infty} \mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\right)\:\mathrm{cos}\:\left(\pi\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx}=? \\ $$

Question Number 166560 Answers: 1 Comments: 0

Question Number 166552 Answers: 0 Comments: 0

∫_(−∞) ^∞ cos ((1/2)πx(x+1)) sin (πx^2 ) dx =?

$$\:\:\:\:\int_{−\infty} ^{\infty} \mathrm{cos}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\pi\mathrm{x}\left(\mathrm{x}+\mathrm{1}\right)\right)\:\mathrm{sin}\:\left(\pi\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx}\:=? \\ $$

Question Number 166542 Answers: 1 Comments: 0

Question Number 166541 Answers: 1 Comments: 0

fin ∫ sec^3 x dx with out using the bart ?

$${fin}\:\int\:{sec}^{\mathrm{3}} {x}\:{dx}\:{with}\:{out}\:{using}\:{the}\:{bart}\:? \\ $$

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