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AllQuestion and Answers: Page 587

Question Number 160873 Answers: 2 Comments: 0

Question Number 160871 Answers: 1 Comments: 0

(((2 (((2(√(13))+5)/( (√5)+2)))^(1/3) +2 (((2(√(13))−5)/( (√5)−2)))^(1/3) +1)^2 −1))^(1/6) =?

$$\:\:\sqrt[{\mathrm{6}}]{\left(\mathrm{2}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}\sqrt{\mathrm{13}}+\mathrm{5}}{\:\sqrt{\mathrm{5}}+\mathrm{2}}}\:+\mathrm{2}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{2}\sqrt{\mathrm{13}}−\mathrm{5}}{\:\sqrt{\mathrm{5}}−\mathrm{2}}}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}}=? \\ $$

Question Number 160869 Answers: 0 Comments: 2

Find: 𝛀 =∫_( 0) ^( ∞) ((x ln (1 + x))/((x + 1)(x^2 + 1))) dx = ?

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx}\:=\:? \\ $$

Question Number 160867 Answers: 0 Comments: 0

A piece of metal in the form of an equilateral triangle that has been subjected to hammering, and its circumference expands at a rate of 6 cm/s so that it remains preserved in its shape. The rate of change in its area when its side length is 12 cm

$$ \\ $$A piece of metal in the form of an equilateral triangle that has been subjected to hammering, and its circumference expands at a rate of 6 cm/s so that it remains preserved in its shape. The rate of change in its area when its side length is 12 cm

Question Number 160866 Answers: 0 Comments: 0

Question Number 160865 Answers: 0 Comments: 1

lim_(x→3) ((tan(x)−tan(3))/(sin(ln(x−2)))) work with the rule of substitution of infinitely small functions equivalent to a limit

$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{3}} {\boldsymbol{\mathrm{lim}}}\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}\left(\mathrm{3}\right)}{\boldsymbol{{sin}}\left(\boldsymbol{{ln}}\left(\boldsymbol{{x}}−\mathrm{2}\right)\right)} \\ $$$$\boldsymbol{{work}}\:\boldsymbol{{with}}\:{the}\:{rule}\:{of} \\ $$$${substitution}\:\:{of}\:{infinitely} \\ $$$${small}\:\:{functions}\:{equivalent}\: \\ $$$${to}\:{a}\:{limit} \\ $$

Question Number 160853 Answers: 1 Comments: 1

Question Number 160852 Answers: 0 Comments: 0

Question Number 160848 Answers: 2 Comments: 0

Find the value of a such that −2 < ((2x+a)/(x^2 +1)) < 2

$${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{a}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:−\mathrm{2}\:<\:\frac{\mathrm{2}{x}+{a}}{{x}^{\mathrm{2}} +\mathrm{1}}\:<\:\mathrm{2} \\ $$

Question Number 160844 Answers: 1 Comments: 0

Question Number 160839 Answers: 2 Comments: 1

Question Number 160837 Answers: 0 Comments: 4

Question Number 160833 Answers: 1 Comments: 0

Σ_(k=1) ^∞ ((cos (ln k))/( (√k))) divergespnt or convergent?

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{cos}\:\left(\mathrm{ln}\:{k}\right)}{\:\sqrt{{k}}} \\ $$$$\mathrm{divergespnt}\:\mathrm{or}\:\mathrm{convergent}? \\ $$

Question Number 160832 Answers: 1 Comments: 0

(√(2021−2(√(2021−2(√(2021−2x)))))) = x x=?

$$\:\sqrt{\mathrm{2021}−\mathrm{2}\sqrt{\mathrm{2021}−\mathrm{2}\sqrt{\mathrm{2021}−\mathrm{2x}}}}\:=\:\mathrm{x} \\ $$$$\:\mathrm{x}=? \\ $$

Question Number 160831 Answers: 0 Comments: 4

simplify ((2+(√5)))^(1/3)

$$\mathrm{simplify}\:\:\sqrt[{\mathrm{3}}]{\mathrm{2}+\sqrt{\mathrm{5}}} \\ $$

Question Number 160829 Answers: 0 Comments: 1

Question Number 160825 Answers: 1 Comments: 0

lim_(n→∞) [∫_0 ^1 (1+sin ((πt)/2))^n dt]^(1/n) =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+\mathrm{sin}\:\frac{\pi\mathrm{t}}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{dt}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} =? \\ $$

Question Number 160823 Answers: 0 Comments: 1

Question Number 160822 Answers: 0 Comments: 0

Question Number 160821 Answers: 1 Comments: 1

Question Number 160816 Answers: 0 Comments: 1

Question Number 160815 Answers: 1 Comments: 1

sec (3x)−6cos (3x)=4sin (3x) find the solution

$$\:\:\:\:\mathrm{sec}\:\left(\mathrm{3x}\right)−\mathrm{6cos}\:\left(\mathrm{3x}\right)=\mathrm{4sin}\:\left(\mathrm{3x}\right) \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 160796 Answers: 1 Comments: 0

lim_(n→∞) (√n)∫_(−∞) ^(+∞) ((cos x)/((1+x^2 )^n ))dx=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{n}}\int_{−\infty} ^{+\infty} \frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }\mathrm{dx}=? \\ $$

Question Number 160798 Answers: 0 Comments: 0

Question Number 160793 Answers: 2 Comments: 0

lim_(x→0) ((2^(cos x) − 2)/x^2 ) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{cos}\:\mathrm{x}} \:−\:\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 160792 Answers: 2 Comments: 0

∫ ((sec x)/( (√(1+2sec x)))) (√((cosec x−cot x)/(cosec x+cot x))) dx =?

$$\:\:\:\int\:\frac{\mathrm{sec}\:\mathrm{x}}{\:\sqrt{\mathrm{1}+\mathrm{2sec}\:\mathrm{x}}}\:\sqrt{\frac{\mathrm{cosec}\:\mathrm{x}−\mathrm{cot}\:\mathrm{x}}{\mathrm{cosec}\:\mathrm{x}+\mathrm{cot}\:\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$

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