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AllQuestion and Answers: Page 493

Question Number 169708 Answers: 0 Comments: 0

Question Number 169565 Answers: 0 Comments: 1

lim_(x→0) ((a^(sinx) −c^(sinx) )/(m^(sinx) −n^(sinx) ))=? ∀{a,c,m,n}∈[0,∞]

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{a}^{{sinx}} −{c}^{{sinx}} }{{m}^{{sinx}} −{n}^{{sinx}} }=? \\ $$$$\forall\left\{{a},{c},{m},{n}\right\}\in\left[\mathrm{0},\infty\right] \\ $$

Question Number 169563 Answers: 0 Comments: 1

Question Number 169559 Answers: 1 Comments: 1

Question Number 169558 Answers: 3 Comments: 0

(dy/dx) = ((2x−y+1)/(x−4y+3))

$$\:\:\:\:\:\:\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}{x}−{y}+\mathrm{1}}{{x}−\mathrm{4}{y}+\mathrm{3}}\:\:\: \\ $$

Question Number 169573 Answers: 0 Comments: 0

find real matrix A such that: t_A ×A=O , where O is null marix

$${find}\:{real}\:{matrix}\:{A}\:{such}\:{that}: \\ $$$${t}_{{A}} ×{A}={O}\:,\:{where}\:{O}\:{is}\:{null}\:{marix} \\ $$

Question Number 169572 Answers: 1 Comments: 0

Question Number 169553 Answers: 1 Comments: 0

solve the D.E 2dx−e^(y−x) dy=0

$${solve}\:{the}\:{D}.{E} \\ $$$$\mathrm{2}{dx}−{e}^{{y}−{x}} {dy}=\mathrm{0} \\ $$

Question Number 169549 Answers: 1 Comments: 0

convert this D.E to exact D.E and solve it ydx+x(1+y)dy=0

$${convert}\:{this}\:{D}.{E}\:{to}\:{exact}\:{D}.{E}\:{and}\:{solve}\:{it} \\ $$$${ydx}+{x}\left(\mathrm{1}+{y}\right){dy}=\mathrm{0} \\ $$

Question Number 169548 Answers: 0 Comments: 1

Question Number 169541 Answers: 1 Comments: 0

Question Number 169539 Answers: 1 Comments: 2

Question Number 169538 Answers: 0 Comments: 1

Question Number 169537 Answers: 0 Comments: 2

Question Number 169533 Answers: 0 Comments: 1

{ ((x+(1/y)=1)),(((1/x)+y=2)) :}⇒x^(2022) +(1/y^(2022) ) =?

$$\:\:\begin{cases}{{x}+\frac{\mathrm{1}}{{y}}=\mathrm{1}}\\{\frac{\mathrm{1}}{{x}}+{y}=\mathrm{2}}\end{cases}\Rightarrow{x}^{\mathrm{2022}} +\frac{\mathrm{1}}{{y}^{\mathrm{2022}} }\:=? \\ $$

Question Number 169527 Answers: 1 Comments: 1

evaluate the limit(if it exists) lim_(n→∞) [(((√(n^4 −2n^3 ))−n^2 )/(n+2))]^3

$$\boldsymbol{{evaluate}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\left(\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{exists}}\right) \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{n}}\rightarrow\infty} \left[\frac{\sqrt{\boldsymbol{{n}}^{\mathrm{4}} −\mathrm{2}\boldsymbol{{n}}^{\mathrm{3}} }−\boldsymbol{{n}}^{\mathrm{2}} }{\boldsymbol{{n}}+\mathrm{2}}\right]^{\mathrm{3}} \\ $$

Question Number 169526 Answers: 1 Comments: 0

solve the D.E. y^′ =tan(x+y)−1

$${solve}\:{the}\:{D}.{E}. \\ $$$${y}^{'} ={tan}\left({x}+{y}\right)−\mathrm{1} \\ $$

Question Number 169508 Answers: 1 Comments: 0

Evaluate if the limit exist lim_(n→∞) (((3^n +(−2)^(n+1) )/(3^(n−2) −2^(2n−1) )))

$${Evaluate}\:{if}\:{the}\:{limit}\:{exist} \\ $$$${lim}_{\boldsymbol{{n}}\rightarrow\infty} \left(\frac{\mathrm{3}^{\boldsymbol{{n}}} +\left(−\mathrm{2}\right)^{\boldsymbol{{n}}+\mathrm{1}} }{\mathrm{3}^{\boldsymbol{{n}}−\mathrm{2}} −\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} }\right) \\ $$

Question Number 169504 Answers: 0 Comments: 1

Question Number 169501 Answers: 1 Comments: 0

Question Number 169498 Answers: 1 Comments: 3

Question Number 169497 Answers: 1 Comments: 0

Determine all functions f:R→R such that af(b)+bf(a)=(a+b)f((√(ab))) ∀ab>0

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}{f}\left(\mathrm{b}\right)+\mathrm{b}{f}\left(\mathrm{a}\right)=\left(\mathrm{a}+\mathrm{b}\right){f}\left(\sqrt{\mathrm{ab}}\right)\:\forall\mathrm{ab}>\mathrm{0} \\ $$

Question Number 169514 Answers: 1 Comments: 2

evaluate the following limit (if it exists) lim_(n→∞) ((ln^2 (n+1))/((n−1)^2 ))

$$\boldsymbol{{evaluate}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{limit}} \\ $$$$\left(\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{exists}}\right) \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{n}}\rightarrow\infty} \frac{\boldsymbol{{ln}}^{\mathrm{2}} \left(\boldsymbol{{n}}+\mathrm{1}\right)}{\left(\boldsymbol{{n}}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 169481 Answers: 0 Comments: 0

Question Number 169480 Answers: 1 Comments: 0

Question Number 169479 Answers: 2 Comments: 2

lim_(x→4) (((cos a)^x −(sin a)^x −cos 2a)/(x−4)) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:{a}\right)^{{x}} −\left(\mathrm{sin}\:{a}\right)^{{x}} −\mathrm{cos}\:\mathrm{2}{a}}{{x}−\mathrm{4}}\:=? \\ $$

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