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Question Number 66010 Answers: 0 Comments: 1

Using Σ_(n=1) ^∞ (1/(n!))=e , prove that lim_(n→∞) (1+(1/n))^n =e

$${Using}\:\sum_{{n}=\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{{n}!}={e}\:,\:{prove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} ={e} \\ $$

Question Number 66005 Answers: 0 Comments: 0

solve x^2 y^(′′) +xy^′ −3y =4e^(−x)

$${solve}\:\:\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} −\mathrm{3}{y}\:=\mathrm{4}{e}^{−{x}} \\ $$

Question Number 66004 Answers: 1 Comments: 0

x^x^x^⋰ =3 find the value of x

$${x}^{{x}^{{x}^{\iddots} } } =\mathrm{3} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x} \\ $$

Question Number 65992 Answers: 1 Comments: 1

x = (1/(3∙1!)) + (1/(4∙2!)) + (1/(5∙3!)) + … + (1/(1002∙1000!)) x∙1000! = ?

$${x}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{1}!}\:+\:\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{3}!}\:+\:\ldots\:+\:\frac{\mathrm{1}}{\mathrm{1002}\centerdot\mathrm{1000}!} \\ $$$${x}\centerdot\mathrm{1000}!\:\:=\:\:? \\ $$

Question Number 65988 Answers: 3 Comments: 1

∫dx/x^2 −x+1

$$\int{dx}/{x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$

Question Number 66041 Answers: 0 Comments: 0

Question Number 65983 Answers: 1 Comments: 1

Simplify (1+ 2i(√2))^7 − (1 +2i)^7

$$\:{Simplify}\: \\ $$$$\:\:\:\left(\mathrm{1}+\:\mathrm{2}{i}\sqrt{\mathrm{2}}\right)^{\mathrm{7}} \:−\:\left(\mathrm{1}\:+\mathrm{2}{i}\right)^{\mathrm{7}} \\ $$

Question Number 65972 Answers: 1 Comments: 0

If ((log_2 a)/(log_3 b))=m and ((log_3 a)/(log_2 b))=n a>1 and b>1 then (m/n)=... a.log_2 3 b. log_3 2 c. log_4 9 d. (log_2 3)^2 e. (log_3 2)^2

Question Number 65971 Answers: 2 Comments: 0

If (a^2 /b^2 )=12 then log(^3 (√(b/a)))=.. a. −2 b. −1 c. 0 d. 1 e. 2

$$\mathrm{If}\:\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{12}\:\mathrm{then}\:\mathrm{log}\left(\:^{\mathrm{3}} \sqrt{\frac{{b}}{{a}}}\right)=.. \\ $$$${a}.\:−\mathrm{2} \\ $$$${b}.\:−\mathrm{1} \\ $$$${c}.\:\mathrm{0} \\ $$$${d}.\:\mathrm{1} \\ $$$${e}.\:\mathrm{2} \\ $$

Question Number 65970 Answers: 1 Comments: 0

log_5 (√(27))×log_9 125+log_(16) 12=... a. ((61)/(36)) b. (9/4) c. ((61)/(20)) d. ((41)/(12)) e. (7/2)

$$\mathrm{log}_{\mathrm{5}} \sqrt{\mathrm{27}}×\mathrm{log}_{\mathrm{9}} \mathrm{125}+\mathrm{log}_{\mathrm{16}} \mathrm{12}=... \\ $$$${a}.\:\frac{\mathrm{61}}{\mathrm{36}} \\ $$$${b}.\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$$${c}.\:\frac{\mathrm{61}}{\mathrm{20}} \\ $$$${d}.\:\frac{\mathrm{41}}{\mathrm{12}} \\ $$$${e}.\:\frac{\mathrm{7}}{\mathrm{2}} \\ $$

Question Number 65961 Answers: 1 Comments: 0

Let (d/dx)(F(x)) = (e^(sin x) /x) , x>0. If ∫_( 1) ^4 ((2 e^(sin x^2 ) )/x) dx = F(k)−F(1), then one of the possible values of k is

$$\mathrm{Let}\:\frac{{d}}{{dx}}\left({F}\left({x}\right)\right)\:=\:\frac{{e}^{\mathrm{sin}\:{x}} }{{x}}\:,\:{x}>\mathrm{0}. \\ $$$$\mathrm{If}\:\underset{\:\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\:{e}^{\mathrm{sin}\:{x}^{\mathrm{2}} } }{{x}}\:{dx}\:=\:{F}\left({k}\right)−{F}\left(\mathrm{1}\right),\:\mathrm{then}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\:{k}\:\:\mathrm{is} \\ $$

Question Number 65951 Answers: 0 Comments: 1

Question Number 65950 Answers: 4 Comments: 0

∫_0 ^( π/2) tan^3 xdx = ?

$$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \mathrm{tan}\:^{\mathrm{3}} {xdx}\:=\:? \\ $$

Question Number 68063 Answers: 1 Comments: 0

Question Number 65981 Answers: 1 Comments: 0

Question Number 65980 Answers: 3 Comments: 1

Question Number 65945 Answers: 0 Comments: 2

pls i need solution plssss...asap n lim ∈ ((r^3 /(r^4 +n^4 ))) n→∞ r=1 please try and understand the way i typed it

$${pls}\:{i}\:{need}\:{solution}\:{plssss}...{asap} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{n} \\ $$$$\:\:\:{lim}\:\:\:\:\:\:\:\:\:\:\:\in\:\:\:\:\left(\frac{{r}^{\mathrm{3}} }{{r}^{\mathrm{4}} +{n}^{\mathrm{4}} }\right) \\ $$$${n}\rightarrow\infty\:\:\:\:\:\:{r}=\mathrm{1} \\ $$$$ \\ $$$${please}\:{try}\:{and}\:{understand}\:{the}\:{way}\:{i}\:{typed}\:{it} \\ $$

Question Number 65959 Answers: 0 Comments: 0

x^5 +ax^3 +bx^2 +cx+d=0 (x^2 +px+q)(x^3 +rx^2 +sx+t)=0 then elimating r,s,t pq(p^2 +a)+d=q(b+2pq) q^2 (p^2 +a)+dp=q(c+q^2 ) please try bringing into single variable sir...

$${x}^{\mathrm{5}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{px}+{q}\right)\left({x}^{\mathrm{3}} +{rx}^{\mathrm{2}} +{sx}+{t}\right)=\mathrm{0} \\ $$$${then}\:{elimating}\:{r},{s},{t}\: \\ $$$$\:{pq}\left({p}^{\mathrm{2}} +{a}\right)+{d}={q}\left({b}+\mathrm{2}{pq}\right) \\ $$$$\:{q}^{\mathrm{2}} \left({p}^{\mathrm{2}} +{a}\right)+{dp}={q}\left({c}+{q}^{\mathrm{2}} \right) \\ $$$${please}\:{try}\:{bringing}\:{into}\:{single} \\ $$$${variable}\:{sir}... \\ $$$$\: \\ $$

Question Number 65934 Answers: 3 Comments: 0

log_7 2=a log_2 3=b log_6 98=...

$$\:\mathrm{log}_{\mathrm{7}} \:\mathrm{2}={a} \\ $$$$\mathrm{log}_{\mathrm{2}} \:\mathrm{3}={b} \\ $$$$\:\mathrm{log}_{\mathrm{6}} \:\mathrm{98}=... \\ $$

Question Number 65931 Answers: 1 Comments: 0

(((log_6 36)^2 −(log_3 4)^2 )/(log_3 ((√(12)))))=...

$$\frac{\left(\mathrm{log}_{\mathrm{6}} \mathrm{36}\right)^{\mathrm{2}} −\left(\mathrm{log}_{\mathrm{3}} \mathrm{4}\right)^{\mathrm{2}} }{\mathrm{log}_{\mathrm{3}} \left(\sqrt{\mathrm{12}}\right)}=... \\ $$

Question Number 65930 Answers: 1 Comments: 0

If t=((x^2 −3)/(3x+7)) then log(1−∣t∣) can to find for a. 2<x<6 b.− 2<x<5 c.− 2≤x≤6 d. x≤−2 or x>6 e. x<−1 or x>3

$$\mathrm{If}\:{t}=\frac{{x}^{\mathrm{2}} −\mathrm{3}}{\mathrm{3}{x}+\mathrm{7}}\:\mathrm{then} \\ $$$$\mathrm{log}\left(\mathrm{1}−\mid{t}\mid\right)\:\mathrm{can}\:\mathrm{to}\:\mathrm{find}\:\mathrm{for} \\ $$$$\mathrm{a}.\:\mathrm{2}<{x}<\mathrm{6} \\ $$$${b}.−\:\mathrm{2}<{x}<\mathrm{5} \\ $$$${c}.−\:\mathrm{2}\leqslant{x}\leqslant\mathrm{6} \\ $$$$\mathrm{d}.\:{x}\leqslant−\mathrm{2}\:\mathrm{or}\:{x}>\mathrm{6} \\ $$$${e}.\:{x}<−\mathrm{1}\:{or}\:{x}>\mathrm{3} \\ $$

Question Number 65929 Answers: 1 Comments: 2

Question Number 65926 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−x) ln(1+x^2 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} {ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 65925 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−2t) ln(1−t)dt

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{−\mathrm{2}{t}} {ln}\left(\mathrm{1}−{t}\right){dt} \\ $$

Question Number 65924 Answers: 0 Comments: 1

calculate ∫_(−(π/6)) ^(π/6) (x/(sinx))dx

$${calculate}\:\int_{−\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{6}}} \:\frac{{x}}{{sinx}}{dx}\: \\ $$

Question Number 65923 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((1−cos(2x^2 ))/x^2 )dx

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

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