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Question Number 71777 Answers: 0 Comments: 1

lim_(n→∞) (((n! + 3^n )/(n^n + 3^n ))) = ?

$$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\left(\frac{\boldsymbol{{n}}!\:+\:\mathrm{3}^{\boldsymbol{{n}}} }{\boldsymbol{{n}}^{\boldsymbol{{n}}} \:+\:\mathrm{3}^{\boldsymbol{{n}}} }\right)\:=\:? \\ $$

Question Number 71776 Answers: 1 Comments: 0

Question Number 71769 Answers: 0 Comments: 3

show that if f is a differentiable function at the point x=a, then f is continuous at x=a.

$${show}\:{that}\:{if}\:{f}\:{is}\:{a}\:{differentiable}\:{function}\:{at}\:{the}\:{point}\:{x}={a},\:{then}\:{f}\:{is}\:{continuous}\:{at}\:{x}={a}. \\ $$

Question Number 71767 Answers: 0 Comments: 0

Let f be continuous on a closed and bounded subset E, then show that f is uniformly continuous.

$${Let}\:{f}\:{be}\:{continuous}\:{on}\:{a}\:{closed}\:{and}\:{bounded}\:{subset}\:{E},\:{then}\:{show}\:{that}\:{f}\:{is}\:{uniformly}\:{continuous}. \\ $$

Question Number 71761 Answers: 0 Comments: 5

Find at least the first four non zero term in a power series expansion about x = 0 for a general solution to z′′ − x^2 z = 0

$$\mathrm{Find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{power} \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{about}\:\:\mathrm{x}\:\:=\:\:\mathrm{0}\:\:\mathrm{for}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\mathrm{to}\:\:\:\:\mathrm{z}''\:\:−\:\:\mathrm{x}^{\mathrm{2}} \mathrm{z}\:\:\:=\:\:\mathrm{0} \\ $$

Question Number 71751 Answers: 0 Comments: 0

Question Number 71750 Answers: 0 Comments: 2

∫ cos^3 θ (1 − sin^3 θ) Using beta function

$$\int\:\mathrm{cos}^{\mathrm{3}} \theta\:\left(\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{3}} \theta\right) \\ $$$$\mathrm{Using}\:\mathrm{beta}\:\mathrm{function} \\ $$

Question Number 71740 Answers: 0 Comments: 1

Derive the expression for the pressure exerted by an ideal gas on the wall of container

$${Derive}\:{the}\:{expression} \\ $$$${for}\:{the}\:{pressure}\:{exerted} \\ $$$${by}\:{an}\:{ideal}\:{gas}\:{on}\:{the} \\ $$$${wall}\:{of}\:{container} \\ $$

Question Number 71739 Answers: 2 Comments: 0

find the asymptote of folium of Descartes x^3 +y^3 =3axy, and a is a constant >0

$${find}\:{the}\:{asymptote}\:{of}\:{folium}\:{of}\: \\ $$$${Descartes}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{3}{axy},\:{and}\:{a}\:{is}\:{a} \\ $$$${constant}\:>\mathrm{0} \\ $$

Question Number 71729 Answers: 1 Comments: 2

find dU if U=x^2 e^(x/y)

$${find}\:{dU}\:\:\:{if}\:\:\:{U}={x}^{\mathrm{2}} {e}^{\frac{{x}}{{y}}} \\ $$$$ \\ $$

Question Number 71724 Answers: 0 Comments: 0

Question Number 71759 Answers: 0 Comments: 2

Question Number 71790 Answers: 1 Comments: 0

Question Number 71756 Answers: 1 Comments: 0

A=((8+3(√(21))))^(1/3) + ((8−3(√(21))))^(1/3) find A

$${A}=\sqrt[{\mathrm{3}}]{\mathrm{8}+\mathrm{3}\sqrt{\mathrm{21}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{8}−\mathrm{3}\sqrt{\mathrm{21}}} \\ $$$$ \\ $$$${find}\:{A} \\ $$

Question Number 71717 Answers: 1 Comments: 3

Question Number 71698 Answers: 1 Comments: 2

Question Number 71695 Answers: 1 Comments: 0

Question Number 71693 Answers: 1 Comments: 0

Question Number 71680 Answers: 1 Comments: 0

Question Number 71674 Answers: 1 Comments: 0

Question Number 71666 Answers: 1 Comments: 1

f:z→z f(x+y)=f(x)+f(y)+3(4xy−1) ,f(1)=0 ∀x,y ∈z evaluate f(19)

$${f}:{z}\rightarrow{z} \\ $$$$ \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{3}\left(\mathrm{4}{xy}−\mathrm{1}\right) \\ $$$$ \\ $$$$,{f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$ \\ $$$$\forall{x},{y}\:\in{z} \\ $$$${evaluate}\:{f}\left(\mathrm{19}\right) \\ $$

Question Number 71665 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((x+1)^2 ((√(x^2 +4)))))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\right)} \\ $$

Question Number 71664 Answers: 1 Comments: 1

find nature of the sequence U_n =(1/n)(Σ_(k=1) ^n (1/k))^2

$${find}\:{nature}\:{of}\:{the}\:{sequence}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\right)^{\mathrm{2}} \\ $$

Question Number 71663 Answers: 1 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) with n integr and n≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 71649 Answers: 0 Comments: 3

Question Number 71645 Answers: 1 Comments: 1

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