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Question Number 103655 Answers: 0 Comments: 3

lim_(x→∞) (−ln((10)/(17)))^(((17)/(10))x) =???

$${li}\underset{{x}\rightarrow\infty} {{m}}\left(−{ln}\frac{\mathrm{10}}{\mathrm{17}}\right)^{\frac{\mathrm{17}}{\mathrm{10}}{x}} =??? \\ $$

Question Number 103654 Answers: 1 Comments: 0

if a,b>1 lim_(x→0^+ ) ((ln(b−x))/(ax))=???

$$\:{if}\:{a},{b}>\mathrm{1}\:\:{li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}}=??? \\ $$

Question Number 103537 Answers: 1 Comments: 0

∫(x/((a^2 cosx+b^2 sinx)))dx

$$\int\frac{\mathrm{x}}{\left(\mathrm{a}^{\mathrm{2}} \mathrm{cosx}+\mathrm{b}^{\mathrm{2}} \mathrm{sinx}\right)}\mathrm{dx} \\ $$

Question Number 103492 Answers: 4 Comments: 1

Q1: Evaluate ∫_(−1) ^( 1) ∣x∣∙(x^3 +1)dx Q2: Find the sum of all integers k for which the equation 2x^3 −6x^2 +k=0 has more than one solution. Q3: Find the shortest distance from a point on the curve y=x^2 −x to the line y=x−3

$$\mathrm{Q1}:\:\:\mathrm{Evaluate}\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} \mid\mathrm{x}\mid\centerdot\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Q2}:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{integers}\:{k}\:\mathrm{for}\: \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} +{k}=\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{solution}. \\ $$$$ \\ $$$$\mathrm{Q3}:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{a}\: \\ $$$$\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:{y}={x}^{\mathrm{2}} −{x}\:\mathrm{to}\:\mathrm{the}\:\mathrm{line} \\ $$$${y}={x}−\mathrm{3} \\ $$

Question Number 103489 Answers: 2 Comments: 0

Question Number 103484 Answers: 0 Comments: 0

Question Number 103483 Answers: 3 Comments: 0

y^2 −u(u+y). (dy/du) = 0

$${y}^{\mathrm{2}} −{u}\left({u}+{y}\right).\:\frac{{dy}}{{du}}\:=\:\mathrm{0} \\ $$

Question Number 103481 Answers: 1 Comments: 0

prove that (cos((nθ)/5)+isin((2nθ)/(10)))^5 −(1/e^(inθ) )=2sin(nθ) ?

$${prove}\:{that}\:\left({cos}\frac{{n}\theta}{\mathrm{5}}+{isin}\frac{\mathrm{2}{n}\theta}{\mathrm{10}}\right)^{\mathrm{5}} −\frac{\mathrm{1}}{{e}^{{in}\theta} }=\mathrm{2}{sin}\left({n}\theta\right)\:? \\ $$

Question Number 103480 Answers: 0 Comments: 0

if f(x)=∣x−1 0<x<1∣ solve in (1)Fourier series of sines only ? (2) Fourier series of cosines ?

$${if}\:{f}\left({x}\right)=\mid{x}−\mathrm{1}\:\:\:\:\:\:\mathrm{0}<{x}<\mathrm{1}\mid\:{solve}\:{in} \\ $$$$ \\ $$$$\left(\mathrm{1}\right){Fourier}\:{series}\:{of}\:{sines}\:{only}\:? \\ $$$$\left(\mathrm{2}\right)\:{Fourier}\:{series}\:{of}\:{cosines}\:? \\ $$

Question Number 103479 Answers: 1 Comments: 0

by ussing laplace find cosh(2t)cos(4t) ?

$${by}\:{ussing}\:{laplace}\:{find}\:{cosh}\left(\mathrm{2}{t}\right){cos}\left(\mathrm{4}{t}\right)\:? \\ $$

Question Number 103478 Answers: 4 Comments: 0

Question Number 103477 Answers: 0 Comments: 0

Question Number 103468 Answers: 2 Comments: 0

(d^2 y/dx^2 ) + 2 (dy/dx) +2y = cos 4x? by UC method

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{2}\:\frac{{dy}}{{dx}}\:+\mathrm{2}{y}\:=\:\mathrm{cos}\:\mathrm{4}{x}? \\ $$$${by}\:{UC}\:{method}\: \\ $$

Question Number 103463 Answers: 2 Comments: 0

lim_(x→∞) ((ln(3e^(2x) +5e^x −2))/(ln(27e^(3x) −1))) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{3}{e}^{\mathrm{2}{x}} +\mathrm{5}{e}^{{x}} −\mathrm{2}\right)}{\mathrm{ln}\left(\mathrm{27}{e}^{\mathrm{3}{x}} −\mathrm{1}\right)}\:? \\ $$

Question Number 103459 Answers: 2 Comments: 6

what are the complex solution tan (z) = −2 ?

$${what}\:{are}\:{the}\:{complex}\:{solution}\:\mathrm{tan} \\ $$$$\left({z}\right)\:=\:−\mathrm{2}\:? \\ $$

Question Number 103458 Answers: 2 Comments: 0

(1)If p and q are the roots quadratic equation x^2 −x−4050 = 0 , find the value of p^2 +q ? (2) if f(x)=((7x+q)/2) and g(x)=7x+8 ; (fog)(4) = 24 . find the value of q

$$\left(\mathrm{1}\right){If}\:{p}\:{and}\:{q}\:{are}\:{the}\:{roots}\:{quadratic} \\ $$$${equation}\:{x}^{\mathrm{2}} −{x}−\mathrm{4050}\:=\:\mathrm{0}\:,\:{find}\:{the}\:{value} \\ $$$${of}\:{p}^{\mathrm{2}} +{q}\:?\: \\ $$$$\left(\mathrm{2}\right)\:{if}\:{f}\left({x}\right)=\frac{\mathrm{7}{x}+{q}}{\mathrm{2}}\:{and}\:{g}\left({x}\right)=\mathrm{7}{x}+\mathrm{8}\:; \\ $$$$\left({fog}\right)\left(\mathrm{4}\right)\:=\:\mathrm{24}\:.\:{find}\:{the}\:{value}\:{of}\:{q} \\ $$

Question Number 103457 Answers: 2 Comments: 0

f(((1−x)/(1+x))) = x+2 then what is the domain and range of f^(−1) (x) ?

$${f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)\:=\:{x}+\mathrm{2}\:{then}\:{what}\:{is}\:{the}\:{domain} \\ $$$${and}\:{range}\:{of}\:{f}^{−\mathrm{1}} \left({x}\right)\:? \\ $$

Question Number 103454 Answers: 1 Comments: 0

∫ (x^2 +2x^4 +3x^6 )(√(1+x^2 +x^4 )) dx

$$\int\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{6}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }\:{dx}\: \\ $$

Question Number 103449 Answers: 1 Comments: 0