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AllQuestion and Answers: Page 1701

Question Number 32441 Answers: 1 Comments: 0

Question Number 32440 Answers: 1 Comments: 0

Question Number 32524 Answers: 0 Comments: 0

(1/2)x^2 +(√2)=

$$\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}= \\ $$

Question Number 32425 Answers: 0 Comments: 0

( (1/(99)) − 1)^(108) + ((2/(99)) − 1)^(107) + ((3/(99)) − 1)^(106) + ... + (((107)/(99)) − 1)^2 + (((108)/(99)) − 1) = ....

$$\left(\:\frac{\mathrm{1}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{108}} \:+\:\left(\frac{\mathrm{2}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{107}} \:+\:\left(\frac{\mathrm{3}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{106}} \:+\:...\:+\:\left(\frac{\mathrm{107}}{\mathrm{99}}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\frac{\mathrm{108}}{\mathrm{99}}\:−\:\mathrm{1}\right)\:\:=\:\:\:.... \\ $$

Question Number 32424 Answers: 1 Comments: 0

Question Number 32423 Answers: 0 Comments: 0

Question Number 32420 Answers: 0 Comments: 0

Question Number 32419 Answers: 0 Comments: 0

$$ \\ $$

Question Number 32418 Answers: 0 Comments: 1

The number of real roots or x^8 − x^5 − x + 1 = 0 is equal to

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{or} \\ $$$${x}^{\mathrm{8}} −\:{x}^{\mathrm{5}} −\:{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 32409 Answers: 1 Comments: 0

Question Number 32407 Answers: 0 Comments: 1

lim_(x→0) ((1−cos (1−cos x))/(x×x×x×x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}} \\ $$

Question Number 32402 Answers: 0 Comments: 1

∫((x+2)/(1−x))

$$\int\frac{{x}+\mathrm{2}}{\mathrm{1}−{x}} \\ $$

Question Number 32401 Answers: 0 Comments: 0

Question Number 32399 Answers: 0 Comments: 0

Question Number 32396 Answers: 1 Comments: 0

roots 2x×x+x+3

$${roots} \\ $$$$\mathrm{2}{x}×\boldsymbol{{x}}+\boldsymbol{{x}}+\mathrm{3} \\ $$

Question Number 32395 Answers: 0 Comments: 1

1+1

$$\mathrm{1}+\mathrm{1} \\ $$

Question Number 32382 Answers: 2 Comments: 2

If the equation ax^2 +2bx−3c=0 has no real roots and (((3c)/4))< a+b, then

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:{ax}^{\mathrm{2}} +\mathrm{2}{bx}−\mathrm{3}{c}=\mathrm{0}\:\mathrm{has} \\ $$$$\mathrm{no}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{and}\:\left(\frac{\mathrm{3}{c}}{\mathrm{4}}\right)<\:{a}+{b},\:\mathrm{then} \\ $$

Question Number 32380 Answers: 1 Comments: 2

Question Number 32379 Answers: 1 Comments: 0

Question Number 32376 Answers: 4 Comments: 1

Question Number 32369 Answers: 0 Comments: 0

prove that n^(−α) ∼ ∫_n ^(n+1) t^(−α) dt 2) prove that Σ_(k=1) ^n (1/k^α ) ∼ (n^(1−α) /(1−α)) if α<1 and Σ_(k=1) ^n (1/k^α ) ∼ ln(n) if α=1 .

$${prove}\:{that}\:\:{n}^{−\alpha} \:\sim\:\int_{{n}} ^{{n}+\mathrm{1}} \:{t}^{−\alpha} {dt} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:\sim\:\:\frac{{n}^{\mathrm{1}−\alpha} }{\mathrm{1}−\alpha}\:{if}\:\:\alpha<\mathrm{1}\:{and} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:\sim\:{ln}\left({n}\right)\:{if}\:\alpha=\mathrm{1}\:. \\ $$

Question Number 32367 Answers: 0 Comments: 0

let α∈R and x^2 ≠1 find the value of f(x) = ∫_0 ^π ln(x^2 −2x cost +1)dt calculate f(x).

$${let}\:\alpha\in{R}\:{and}\:{x}^{\mathrm{2}} \neq\mathrm{1}\:\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right){dt} \\ $$$${calculate}\:{f}\left({x}\right). \\ $$

Question Number 32365 Answers: 0 Comments: 3

let F(x) = ∫_0 ^π ln(1+xcosθ)dθ .with ∣x∣<1 find F(x) .

$${let}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:{ln}\left(\mathrm{1}+{xcos}\theta\right){d}\theta\:.{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${find}\:{F}\left({x}\right)\:. \\ $$

Question Number 32364 Answers: 0 Comments: 1

let u_n = (e −(1+(1/n))^n )^((√(n^2 +2)) −(√(n^2 +1))) find lim u_n

$${let}\:\:{u}_{{n}} =\:\left({e}\:−\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right)^{\sqrt{{n}^{\mathrm{2}} \:+\mathrm{2}}\:\:−\sqrt{{n}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$$${find}\:\:{lim}\:{u}_{{n}} \\ $$

Question Number 32363 Answers: 0 Comments: 1

let consider the function f(x,θ) = ∫_x ^x^2 ln( 2+sinθ cost)dt calculate (∂f/∂x)(x,θ) and (∂f/∂θ)(x,θ) .

$${let}\:{consider}\:{the}\:{function} \\ $$$${f}\left({x},\theta\right)\:=\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } {ln}\left(\:\mathrm{2}+{sin}\theta\:{cost}\right){dt} \\ $$$${calculate}\:\frac{\partial{f}}{\partial{x}}\left({x},\theta\right)\:{and}\:\:\frac{\partial{f}}{\partial\theta}\left({x},\theta\right)\:. \\ $$

Question Number 32362 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)(2x+3)(2x+5))) .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)\left(\mathrm{2}{x}+\mathrm{5}\right)}\:. \\ $$

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