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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

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

Question Number 65922 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((sin(3x^2 ))/x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left(\mathrm{3}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx}\: \\ $$

Question Number 65920 Answers: 1 Comments: 1

fnd ∫ (dx/(x+2−(√(3+x^2 ))))

$${fnd}\:\int\:\frac{{dx}}{{x}+\mathrm{2}−\sqrt{\mathrm{3}+{x}^{\mathrm{2}} }} \\ $$

Question Number 65919 Answers: 1 Comments: 1

find ∫ (dx/(x(√(x+1)) +(x+1)(√x))) 2) calculate ∫_1 ^(√3) (dx/(x(√(x+1)) +(x+1)(√x)))

$${find}\:\:\int\:\:\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\:+\left({x}+\mathrm{1}\right)\sqrt{{x}}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}} \:\:\:\frac{{dx}}{{x}\sqrt{{x}+\mathrm{1}}\:+\left({x}+\mathrm{1}\right)\sqrt{{x}}} \\ $$

Question Number 65918 Answers: 1 Comments: 1

simplify A_n =(2+i(√5))^n +(2−i(√5))^n and B_n =(2+i(√5))^n −(2−i(√5))^n

$${simplify}\:{A}_{{n}} =\left(\mathrm{2}+{i}\sqrt{\mathrm{5}}\right)^{{n}} \:+\left(\mathrm{2}−{i}\sqrt{\mathrm{5}}\right)^{{n}} \\ $$$${and}\:{B}_{{n}} =\left(\mathrm{2}+{i}\sqrt{\mathrm{5}}\right)^{{n}} −\left(\mathrm{2}−{i}\sqrt{\mathrm{5}}\right)^{{n}} \\ $$

Question Number 65917 Answers: 0 Comments: 0

prove that 1 +(1/2) +(1/3) +...+(1/n) =(p_n /(2q_n )) with p_n odd

$${prove}\:{that}\:\mathrm{1}\:+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+...+\frac{\mathrm{1}}{{n}}\:=\frac{{p}_{{n}} }{\mathrm{2}{q}_{{n}} }\:\:{with}\:{p}_{{n}} {odd} \\ $$

Question Number 65916 Answers: 0 Comments: 0

solve inside N and Z the equation (1/x)+(1/y)=(1/(15))

$${solve}\:{inside}\:{N}\:{and}\:{Z}\:\:{the}\:{equation}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{\mathrm{15}} \\ $$

Question Number 65915 Answers: 0 Comments: 0

let p prime not 0 and n integr /1≤n<p prove that (((p−1)(p−2)....(p−n))/(n!)) −(−1)^n is integr and divided by p

$${let}\:{p}\:{prime}\:{not}\:\mathrm{0}\:\:{and}\:{n}\:{integr}\:/\mathrm{1}\leqslant{n}<{p}\:{prove}\:{that} \\ $$$$\frac{\left({p}−\mathrm{1}\right)\left({p}−\mathrm{2}\right)....\left({p}−{n}\right)}{{n}!}\:−\left(−\mathrm{1}\right)^{{n}} \:\:{is}\:{integr}\:{and}\:{divided}\:{by}\:{p} \\ $$

Question Number 65914 Answers: 0 Comments: 0

x^n +y^n =z^n make n the subject of formula please help

$${x}^{{n}} +{y}^{{n}} ={z}^{{n}} \:\: \\ $$$${make}\:{n}\:{the}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$${please}\:{help} \\ $$

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