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Question Number 191921 Answers: 1 Comments: 0

Question Number 191889 Answers: 2 Comments: 0

Σ_(n=1) ^k (1/(n^2 +2n)) =?

$$\:\:\:\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{k}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2n}}\:=? \\ $$

Question Number 191887 Answers: 3 Comments: 0

Question Number 191874 Answers: 1 Comments: 0

lim_(x⇒∞) ((e^(x+1) +pi^(x−1) )/(e^(x−1) +pi^(x+1) ))

$${lim}_{{x}\Rightarrow\infty} \frac{{e}^{{x}+\mathrm{1}} +{pi}^{{x}−\mathrm{1}} }{{e}^{{x}−\mathrm{1}} +{pi}^{{x}+\mathrm{1}} } \\ $$$$ \\ $$

Question Number 191873 Answers: 4 Comments: 0

Question Number 191868 Answers: 2 Comments: 0

A particle of mass m moves under the central repulsive force ((mb)/r^3 ) and is initially moving at a distance ′a′ from the origin of a force with velocity ′v′ at right angle to ′a′. show that rcos pθ=a where p =(b/(a^2 v^2 ))+1.

$${A}\:{particle}\:{of}\:{mass}\:{m}\:{moves}\:{under}\:{the}\:{central} \\ $$$${repulsive}\:{force}\:\frac{{mb}}{{r}^{\mathrm{3}} }\:\:{and}\:{is}\:{initially}\:{moving} \\ $$$${at}\:{a}\:{distance}\:'{a}'\:\:{from}\:{the}\:{origin}\:{of}\:\:{a}\:{force} \\ $$$${with}\:{velocity}\:\:'{v}'\:{at}\:{right}\:{angle}\:{to}\:\:'{a}'. \\ $$$${show}\:{that}\:\:\: \\ $$$$\:\:\:\:\:{r}\mathrm{cos}\:{p}\theta={a}\:\:{where}\:{p}\:=\frac{{b}}{{a}^{\mathrm{2}} {v}^{\mathrm{2}} }+\mathrm{1}. \\ $$$$ \\ $$

Question Number 191867 Answers: 1 Comments: 0

Prove that if u=f(x^3 +y^3 ),where f is arbitry function then x^2 (∂u/∂y) = y^2 (∂u/∂x)

$${Prove}\:{that}\:{if}\:\:\:{u}={f}\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} \right),{where}\:{f}\:\:{is}\:{arbitry} \\ $$$${function}\:{then}\:\:\:\:{x}^{\mathrm{2}} \:\frac{\partial{u}}{\partial{y}}\:=\:{y}^{\mathrm{2}} \frac{\partial{u}}{\partial{x}} \\ $$

Question Number 191862 Answers: 1 Comments: 1

Find the last digit from (2^(400) −2^(320) )(2^(200) +2^(160) )(2^(200) −2^(160) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{from}\: \\ $$$$\:\left(\mathrm{2}^{\mathrm{400}} −\mathrm{2}^{\mathrm{320}} \right)\left(\mathrm{2}^{\mathrm{200}} +\mathrm{2}^{\mathrm{160}} \right)\left(\mathrm{2}^{\mathrm{200}} −\mathrm{2}^{\mathrm{160}} \right) \\ $$

Question Number 191859 Answers: 1 Comments: 1

Question Number 191856 Answers: 1 Comments: 0

Question Number 191855 Answers: 0 Comments: 0

Question Number 191854 Answers: 1 Comments: 0

Question Number 191846 Answers: 1 Comments: 0

find the last three digits of 4^2^(42) Mohammed Alwan

$${find}\:{the}\:{last}\:{three}\:{digits} \\ $$$${of}\:\mathrm{4}^{\mathrm{2}^{\mathrm{42}} } \\ $$$${Mohammed}\:{Alwan} \\ $$

Question Number 191841 Answers: 2 Comments: 0

Question Number 191840 Answers: 0 Comments: 0

calcul ∫_0 ^1 2∣cosu∣(√(1+3u^2 ))du

$${calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{2}\mid{cosu}\mid\sqrt{\mathrm{1}+\mathrm{3}{u}^{\mathrm{2}} \:}{du} \\ $$

Question Number 191839 Answers: 1 Comments: 0

2^a = 3^b = 36^c then prove that ab = 2c(a + b).

$$\mathrm{2}^{{a}} \:=\:\mathrm{3}^{{b}} \:=\:\mathrm{36}^{{c}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${ab}\:=\:\mathrm{2}{c}\left({a}\:+\:{b}\right). \\ $$

Question Number 191833 Answers: 3 Comments: 0

Question Number 191832 Answers: 0 Comments: 0

Question Number 191831 Answers: 1 Comments: 0

Question Number 191830 Answers: 0 Comments: 0

Question Number 191821 Answers: 1 Comments: 0

Q ▶ Show that: Σ_(i=1) ^(2n) (−1)^(i+1) (1/i)=Σ_(i=1) ^n (1/(i+n))

$$\:{Q}\:\blacktriangleright\:{Show}\:{that}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} \frac{\mathrm{1}}{{i}}=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{i}+{n}} \\ $$

Question Number 191804 Answers: 2 Comments: 1

Question Number 191811 Answers: 2 Comments: 0

∫x^2 e^(−x) dx=?

$$\int{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$

Question Number 191798 Answers: 2 Comments: 2

Question Number 191796 Answers: 2 Comments: 1

Question Number 191795 Answers: 1 Comments: 1

3^x −2^x =19 x=??

$$\mathrm{3}^{\mathrm{x}} −\mathrm{2}^{\mathrm{x}} =\mathrm{19} \\ $$$$\mathrm{x}=?? \\ $$

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