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Question Number 165815 Answers: 1 Comments: 0

deteminer l′expression de g(x) g(x)=Σ_(n=1) ^(+oo) (((−1)^n )/n)x^n

$${deteminer}\:{l}'{expression}\:{de}\:{g}\left({x}\right) \\ $$$${g}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}{x}^{{n}} \\ $$

Question Number 165808 Answers: 1 Comments: 0

Which of the following is an even function? A. f_1 (x)= ((sin x)/(3^x +3^(−x) )) B. f_2 (x)= ((cos x)/(3^x +3^(−x) )) C. f_3 (x)=log_(10) (x+(√(x^2 +1))) D. f_4 (x)= (x^2 /(10^x −1))

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{function}? \\ $$$$\mathrm{A}.\:{f}_{\mathrm{1}} \left({x}\right)=\:\frac{\mathrm{sin}\:{x}}{\mathrm{3}^{{x}} +\mathrm{3}^{−{x}} }\:\:\:\:\:\:\:\:\:\mathrm{B}.\:{f}_{\mathrm{2}} \left({x}\right)=\:\frac{\mathrm{cos}\:{x}}{\mathrm{3}^{{x}} +\mathrm{3}^{−{x}} } \\ $$$$\mathrm{C}.\:{f}_{\mathrm{3}} \left({x}\right)=\mathrm{log}_{\mathrm{10}} \left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$\mathrm{D}.\:{f}_{\mathrm{4}} \left({x}\right)=\:\frac{{x}^{\mathrm{2}} }{\mathrm{10}^{{x}} −\mathrm{1}} \\ $$

Question Number 165805 Answers: 1 Comments: 0

If function f(x)=log_(x/2) log_(1/3) log _4 x exist, find the domain of f .

$$\mathrm{If}\:\:\mathrm{function}\:{f}\left({x}\right)=\mathrm{log}_{\frac{{x}}{\mathrm{2}}} \mathrm{log}_{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{log}\:_{\mathrm{4}} \:{x}\:\mathrm{exist}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:{f}\:. \\ $$

Question Number 165804 Answers: 1 Comments: 0

Question Number 165799 Answers: 2 Comments: 0

(4.2)^x =100

$$\left(\mathrm{4}.\mathrm{2}\right)^{{x}} =\mathrm{100} \\ $$$$ \\ $$$$ \\ $$

Question Number 165795 Answers: 2 Comments: 0

Question Number 165794 Answers: 2 Comments: 0

∫(t/e^(−2t) )dt

$$\int\frac{{t}}{{e}^{−\mathrm{2}{t}} }{dt} \\ $$

Question Number 165791 Answers: 2 Comments: 0

Question Number 165787 Answers: 2 Comments: 0

find ∫cos^3 x dx ?

$${find}\:\:\int{cos}^{\mathrm{3}} {x}\:{dx}\:? \\ $$

Question Number 165780 Answers: 0 Comments: 8

Mr and Mr young borrowed Z amount of money from a bank at a daily interest rate r. The youngs make the same micro payment of D amount to the bank each day. Set up a differential equation for amount x owed to the bank at the end of the each day after the loan closing.

$$\mathrm{Mr}\:\mathrm{and}\:\mathrm{Mr}\:\mathrm{young}\:\mathrm{borrowed}\:\mathrm{Z}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{money}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{bank}\:\mathrm{at}\:\mathrm{a}\:\mathrm{daily}\:\mathrm{interest}\:\mathrm{rate}\:\mathrm{r}.\:\mathrm{The}\:\mathrm{youngs}\:\mathrm{make}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{micro}\:\mathrm{payment}\:\mathrm{of}\:\mathrm{D}\:\mathrm{amount}\:\mathrm{to}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{each}\:\mathrm{day}. \\ $$$$\:\mathrm{Set}\:\mathrm{up}\:\mathrm{a}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{amount}\:\mathrm{x}\:\mathrm{owed} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{each}\:\mathrm{day}\:\mathrm{after}\:\mathrm{the}\:\mathrm{loan} \\ $$$$\mathrm{closing}. \\ $$

Question Number 165778 Answers: 1 Comments: 0

solve for the values of m,n and l l+m+n=0 l^2 +m^2 −n^2 =0

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m},\mathrm{n}\:\mathrm{and}\:\mathrm{l} \\ $$$$\mathrm{l}+\mathrm{m}+\mathrm{n}=\mathrm{0} \\ $$$$\mathrm{l}^{\mathrm{2}} +\mathrm{m}^{\mathrm{2}} −\mathrm{n}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 165774 Answers: 1 Comments: 0

Question Number 165757 Answers: 1 Comments: 0

Question Number 165756 Answers: 0 Comments: 0

Let M be a compact smooth manifold of dimension d. Prove that there exists some n ∈Z^+ such that M can be regularly embedded in the Euclidean space R^n .

$$\mathrm{Let}\:{M}\:\mathrm{be}\:\mathrm{a}\:\mathrm{compact}\:\mathrm{smooth}\:\mathrm{manifold}\:\mathrm{of}\:\mathrm{dimension}\:{d}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:\mathrm{some}\:{n}\:\in\mathbb{Z}^{+} \:\mathrm{such}\:\mathrm{that}\:{M}\:\mathrm{can}\:\mathrm{be}\:\mathrm{regularly}\:\mathrm{embedded}\:\mathrm{in}\:\mathrm{the}\:\mathrm{Euclidean}\:\mathrm{space}\:\mathbb{R}^{{n}} . \\ $$

Question Number 165777 Answers: 1 Comments: 0

The sum of first the n terms of a series {a_n } is given by S_n =3n^2 +n, find Σ_(k=10) ^(20) a_k . A) 910 B) 913 C) 968 D) 1256

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{the}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series} \\ $$$$\left\{{a}_{{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{S}_{{n}} =\mathrm{3}{n}^{\mathrm{2}} +{n},\:\mathrm{find}\:\underset{{k}=\mathrm{10}} {\overset{\mathrm{20}} {\sum}}{a}_{{k}} \:. \\ $$$$\left.\mathrm{A}\right)\:\mathrm{910} \\ $$$$\left.\mathrm{B}\right)\:\mathrm{913} \\ $$$$\left.\mathrm{C}\right)\:\mathrm{968} \\ $$$$\left.\mathrm{D}\right)\:\mathrm{1256}\: \\ $$

Question Number 165776 Answers: 2 Comments: 0

Solve the equation (√(((√x)+1^ )/( (√x)−1 )))−(√(((√x)−1^ )/( (√x)+1 ))) = 1

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\sqrt{\frac{\sqrt{{x}}+\mathrm{1}^{} }{\:\sqrt{{x}}−\mathrm{1}\:}}−\sqrt{\frac{\sqrt{{x}}−\mathrm{1}^{} }{\:\sqrt{{x}}+\mathrm{1}\:}}\:=\:\mathrm{1} \\ $$

Question Number 165746 Answers: 1 Comments: 0

compute the extreme points of: f=e^x sin(x+y)

$${compute}\:{the}\:{extreme}\:{points}\:{of}:\: \\ $$$${f}={e}^{{x}} {sin}\left({x}+{y}\right) \\ $$

Question Number 165744 Answers: 2 Comments: 0