Question and Answers Forum

AllQuestion and Answers: Page 1211

Question Number 91640 Answers: 0 Comments: 1

find nature of the serie Σ_n cos(πn^2 ln(1+(1/n)))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}} \:{cos}\left(\pi{n}^{\mathrm{2}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right) \\ $$

Question Number 91639 Answers: 0 Comments: 1

find lim_(n→∞) (1+(1/n))^2 ((n!)/n^(n+(1/2)) )

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

Question Number 91638 Answers: 1 Comments: 0

Find the general term: Σ_(n=1) ^k n^n

$${Find}\:{the}\:{general}\:{term}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}{n}^{{n}} \\ $$

Question Number 91637 Answers: 0 Comments: 0

f continue on [0,1] stady the serie Σ u_n with u_n =(−1)^n ∫_0 ^1 t^n f)t)dt

$${f}\:{continue}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:{stady}\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \:\:\:{with} \\ $$$$\left.{u}_{{n}} \left.=\left(−\mathrm{1}\right)^{{n}} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:{t}^{{n}} {f}\right){t}\right){dt} \\ $$

Question Number 91636 Answers: 0 Comments: 0

∫(dx/(x((√x)+^5 (√x^2 ))))

$$\int\frac{{dx}}{{x}\left(\sqrt{{x}}+^{\mathrm{5}} \sqrt{{x}^{\mathrm{2}} }\right)} \\ $$

Question Number 91635 Answers: 0 Comments: 2

given f(x)=log_(10) (x) and log_(10) (102)≈2.0086 , which is closest to f ′(100)? A. 0.0043 B.0.0086 C. 0.01 E. 1.0043

$${given}\:{f}\left({x}\right)=\mathrm{log}_{\mathrm{10}} \left({x}\right)\:{and}\:\mathrm{log}_{\mathrm{10}} \left(\mathrm{102}\right)\approx\mathrm{2}.\mathrm{0086} \\ $$$$,\:{which}\:{is}\:{closest}\:{to}\:{f}\:'\left(\mathrm{100}\right)? \\ $$$${A}.\:\mathrm{0}.\mathrm{0043}\:\:\:\:\:\:{B}.\mathrm{0}.\mathrm{0086} \\ $$$${C}.\:\mathrm{0}.\mathrm{01}\:\:\:\:\:\:\:\:\:\:{E}.\:\mathrm{1}.\mathrm{0043} \\ $$

Question Number 91632 Answers: 0 Comments: 1

find a equivalent of U_n =1+(1/(√2))+(1/(√3))+...+(1/(√n))

$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:=\mathrm{1}+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}+...+\frac{\mathrm{1}}{\sqrt{{n}}} \\ $$

Question Number 91631 Answers: 0 Comments: 1

find a equivalent of Σ_(k=2) ^n ln(k)

$${find}\:{a}\:{equivalent}\:{of}\:\sum_{{k}=\mathrm{2}} ^{{n}} {ln}\left({k}\right) \\ $$

Question Number 91630 Answers: 0 Comments: 1

show that ∫_(−(π/4)) ^(π/4) ((sin2x)/((2+cos2x)^2 ))ln(1+e^x )dx =(π/(16))−((π(√3))/(36))

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$

Question Number 91624 Answers: 0 Comments: 4

Question Number 91622 Answers: 2 Comments: 1

((d(x!))/dx)=

$$\frac{\mathrm{d}\left(\mathrm{x}!\right)}{\mathrm{dx}}= \\ $$

Question Number 91621 Answers: 0 Comments: 1

calculate ∫_0 ^∞ sin(x^6 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{6}} \right){dx} \\ $$

Question Number 91620 Answers: 0 Comments: 1

let f(x) =2 x−(√(x−1)) find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ln(((f(x))/(f^(−1) (x))))dx

$${let}\:{f}\left({x}\right)\:=\mathrm{2}\:{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:\:{and}\:\:\int\:{ln}\left(\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}\right){dx} \\ $$

Question Number 91619 Answers: 0 Comments: 1

calculate ∫_2 ^(+∞) (((−1)^([2x]) )/(x[x]−1))dx

$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\left[\mathrm{2}{x}\right]} }{{x}\left[{x}\right]−\mathrm{1}}{dx} \\ $$

Question Number 91615 Answers: 0 Comments: 2

hi every one is it right if we use tylor in this integration and if there were another way that will be very cool ∫sin(x^4 )dx

$${hi}\:{every}\:{one}\:{is}\:{it}\:{right}\:{if}\:{we}\:{use}\:{tylor} \\ $$$${in}\:{this}\:{integration}\:{and}\:{if}\:{there}\:{were} \\ $$$${another}\:{way}\:{that}\:{will}\:{be}\:{very}\:{cool} \\ $$$$\int{sin}\left({x}^{\mathrm{4}} \right){dx}\: \\ $$$$ \\ $$$$ \\ $$

Question Number 91613 Answers: 1 Comments: 4

solve without using l′hopital lim_(x→e) ((ln(x)−1)/((e/x)−1))

$${solve}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow{e}} {{lim}}\frac{{ln}\left({x}\right)−\mathrm{1}}{\frac{{e}}{{x}}−\mathrm{1}} \\ $$

Question Number 91611 Answers: 0 Comments: 1

find the volume of the region between curves (xy=4 and x+y=5) revolvex around the X axis

$$\:{find}\:{the}\:{volume}\:{of}\:{the}\:{region}\: \\ $$$${between}\:{curves}\:\left({xy}=\mathrm{4}\:{and}\:{x}+{y}=\mathrm{5}\right) \\ $$$${revolvex}\:{around}\:{the}\:{X}\:{axis} \\ $$

Question Number 91608 Answers: 0 Comments: 2

Question Number 91604 Answers: 0 Comments: 0

Question Number 91603 Answers: 0 Comments: 1

calculate ∫_0 ^∞ xe^(−x^2 −[x]) dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} {xe}^{−{x}^{\mathrm{2}} −\left[{x}\right]} \:{dx} \\ $$

Question Number 91599 Answers: 0 Comments: 1

Question Number 91595 Answers: 1 Comments: 2

what′s meaning of (x^. ) or (x^(..) )? are (x^. )=x′?

$$\mathrm{what}'\mathrm{s}\:\mathrm{meaning}\:\mathrm{of}\:\left(\overset{.} {\mathrm{x}}\right)\:\mathrm{or}\:\left(\overset{..} {\mathrm{x}}\right)? \\ $$$$\mathrm{are}\:\left(\overset{.} {\mathrm{x}}\right)=\mathrm{x}'? \\ $$

Question Number 91593 Answers: 1 Comments: 0

∫ ((sec x csc x dx)/(ln(tan^2 x))) ?

$$\int\:\frac{\mathrm{sec}\:{x}\:{csc}\:{x}\:{dx}}{\mathrm{ln}\left(\mathrm{tan}\:^{\mathrm{2}} {x}\right)}\:? \\ $$

Question Number 91588 Answers: 0 Comments: 2

what is f^(−1) for f(x)=⌊x⌋??

$${what}\:{is}\:{f}^{−\mathrm{1}} \:{for}\:{f}\left({x}\right)=\lfloor{x}\rfloor?? \\ $$

Question Number 91578 Answers: 0 Comments: 2

f((1/x))+2f(x)= ((4x^3 +6x)/(3x^2 )) f(x)=?

$$ \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)+\mathrm{2}{f}\left({x}\right)=\:\frac{\mathrm{4}{x}^{\mathrm{3}} +\mathrm{6}{x}}{\mathrm{3}{x}^{\mathrm{2}} } \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 91568 Answers: 2 Comments: 0

Pg 1206 Pg 1207 Pg 1208 Pg 1209 Pg 1210 Pg 1211 Pg 1212 Pg 1213 Pg 1214 Pg 1215

Contact: info@tinkutara.com