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Question Number 98016    Answers: 1   Comments: 3

∫_0 ^1 ((ln^2 (x))/(x^2 +1)) dx ?

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

Question Number 98008    Answers: 0   Comments: 1

Question Number 98004    Answers: 0   Comments: 1

lim_(n→∞) [sin(n)+4^n ×(3/n^2 )×((n+1)/(n^2 −4))]

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{sin}\left(\mathrm{n}\right)+\mathrm{4}^{\mathrm{n}} ×\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} }×\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4}}\right] \\ $$

Question Number 98003    Answers: 4   Comments: 0

prove that E=mc^2

$${prove}\:{that}\: \\ $$$${E}={mc}^{\mathrm{2}} \:\: \\ $$

Question Number 97994    Answers: 1   Comments: 0

find all the values of θ, in the interval 0≤θ≤2π for which sin 3θ−sin θ=(√(3cos 2θ))

$${find}\:{all}\:{the}\:{values}\:{of}\:\theta,\:{in}\:{the}\:{interval}\:\mathrm{0}\leqslant\theta\leqslant\mathrm{2}\pi \\ $$$${for}\:{which}\:\mathrm{sin}\:\mathrm{3}\theta−\mathrm{sin}\:\theta=\sqrt{\mathrm{3cos}\:\mathrm{2}\theta} \\ $$

Question Number 97990    Answers: 1   Comments: 0

find lim_(x→1^+ ) ∫_x ^x^2 ((lnt)/((t−1)^2 ))dt

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}} ^{\mathrm{x}^{\mathrm{2}} } \:\:\frac{\mathrm{lnt}}{\left(\mathrm{t}−\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dt} \\ $$

Question Number 97988    Answers: 0   Comments: 0

calculate by recurrence A_n =∫_0 ^(π/4) (dx/(cos^n x))

$$\mathrm{calculate}\:\mathrm{by}\:\mathrm{recurrence}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{cos}^{\mathrm{n}} \mathrm{x}} \\ $$

Question Number 97987    Answers: 1   Comments: 0

find lim_(n→+∞) Σ_(k=1) ^n (√((n−k)/(n^3 −n^2 k)))

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \sqrt{\frac{\mathrm{n}−\mathrm{k}}{\mathrm{n}^{\mathrm{3}} −\mathrm{n}^{\mathrm{2}} \mathrm{k}}} \\ $$

Question Number 97985    Answers: 2   Comments: 0

let S_n =Σ_(k=1) ^n (1/(√(n^2 +2kn))) find lim_(n→+∞) S_n

$$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{S}_{\mathrm{n}} \\ $$

Question Number 97984    Answers: 2   Comments: 0

calculate Σ_(k=0) ^n (((−1)^k )/(2k+1)) C_n ^k

$$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2k}+\mathrm{1}}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \\ $$

Question Number 97983    Answers: 0   Comments: 0

f continue on [0,1] and f(x)>0 on [0,1] prove that ∫_0 ^1 lnf(x)dx≤ln(∫_0 ^1 f(x)dx)

$$\mathrm{f}\:\mathrm{continue}\:\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)>\mathrm{0}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lnf}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{ln}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right) \\ $$

Question Number 97981    Answers: 1   Comments: 0

calculate lim_(x→1^+ ) ∫_(x−1) ^(x^2 −1) (dt/(ln(1+t)))

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}−\mathrm{1}} ^{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \:\frac{\mathrm{dt}}{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)} \\ $$

Question Number 97979    Answers: 0   Comments: 0

find lim_(n→+∞) (C_(2n) ^n )^(1/n)

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\left(\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 97972    Answers: 3   Comments: 0

Prove that, (d/dx)(e^x ) = e^x

$$\:\:\:\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\:=\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \\ $$

Question Number 97968    Answers: 1   Comments: 1

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Question Number 99300    Answers: 1   Comments: 0

Find Σ_(n=1) ^∞ (1/((3n)!))=?

$$\mathrm{Find}\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}\right)!}=? \\ $$

Question Number 97963    Answers: 0   Comments: 0

Question Number 97956    Answers: 1   Comments: 0

prove Σ_(n=1) ^∞ ((9n+4)/(3n(3n+1)(3n+2)))=(3/2)−ln(3)

$${prove} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{9}{n}+\mathrm{4}}{\mathrm{3}{n}\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\frac{\mathrm{3}}{\mathrm{2}}−{ln}\left(\mathrm{3}\right) \\ $$

Question Number 97953    Answers: 1   Comments: 3

Question Number 97942    Answers: 2   Comments: 0

Question Number 97936    Answers: 1   Comments: 1

Find the value of (√(45−(√(2000)) )) + (√(45+(√(2000))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{45}−\sqrt{\mathrm{2000}}\:}\:\:+\:\:\sqrt{\mathrm{45}+\sqrt{\mathrm{2000}}}\: \\ $$

Question Number 97929    Answers: 0   Comments: 1

Find equation of line through A(1,2,3) and parallel to y axis ?

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{line}\:\mathrm{through}\:\mathrm{A}\left(\mathrm{1},\mathrm{2},\mathrm{3}\right) \\ $$$$\mathrm{and}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{y}\:\mathrm{axis}\:?\: \\ $$

Question Number 97928    Answers: 1   Comments: 0

find the general formula ∫_0 ^(π/2) tan^α (x) dx

$${find}\:{the}\:{general}\:{formula} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\alpha} \left({x}\right)\:{dx} \\ $$

Question Number 97922    Answers: 1   Comments: 0

y′′ + y = cot x

$$\mathrm{y}''\:+\:\mathrm{y}\:=\:\mathrm{cot}\:{x}\: \\ $$

Question Number 97918    Answers: 0   Comments: 1

Deleted one of the previous post. There is an option in app where you can use preferred font size. Soon another option will be added where you will able to use your preferred color combination.

$$\mathrm{Deleted}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{previous}\:\mathrm{post}.\: \\ $$$$\mathrm{There}\:\mathrm{is}\:\mathrm{an}\:\mathrm{option}\:\mathrm{in}\:\mathrm{app}\:\mathrm{where} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{use}\:\mathrm{preferred}\:\mathrm{font}\:\mathrm{size}. \\ $$$$\mathrm{Soon}\:\mathrm{another}\:\mathrm{option}\:\mathrm{will}\:\mathrm{be}\:\mathrm{added} \\ $$$$\mathrm{where}\:\mathrm{you}\:\mathrm{will}\:\mathrm{able}\:\mathrm{to}\:\mathrm{use}\:\mathrm{your} \\ $$$$\mathrm{preferred}\:\mathrm{color}\:\mathrm{combination}. \\ $$

Question Number 97920    Answers: 0   Comments: 4

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