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Question Number 94257    Answers: 2   Comments: 0

If 9y^2 + (1/y^2 ) =3, then find the value of 27y^3 + (1/y^3 )

$$\mathrm{If}\:\mathrm{9y}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:=\mathrm{3},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{27y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} } \\ $$

Question Number 94245    Answers: 1   Comments: 0

find the function f(x) satisfying the given conditions (i)f^′ (x)=4x^2 −1 , f(0)=3 ? (ii)f^(′′) (x)=12 , f^′ (0)=2 , f(0)=3 ? (iii)f^(′′) (x)=2x , f^′ (0)=−3 , f(0)=2 ? help me sir pleas ?

$${find}\:{the}\:{function}\:{f}\left({x}\right)\:{satisfying}\:{the}\:{given}\:{conditions} \\ $$$$\left({i}\right){f}^{'} \left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{3}\:? \\ $$$$\left({ii}\right){f}^{''} \left({x}\right)=\mathrm{12}\:\:,\:{f}^{'} \left(\mathrm{0}\right)=\mathrm{2}\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{3}\:? \\ $$$$\left({iii}\right){f}^{''} \left({x}\right)=\mathrm{2}{x}\:\:,\:\:{f}^{'} \left(\mathrm{0}\right)=−\mathrm{3}\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{2}\:? \\ $$$$ \\ $$$${help}\:{me}\:{sir}\:{pleas}\:? \\ $$

Question Number 94241    Answers: 1   Comments: 1

Prove that arctan(x)+2arctan((√(1+x^2 ))−x)=(π/2)

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\mathrm{arctan}\left(\mathrm{x}\right)+\mathrm{2arctan}\left(\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{x}\right)=\frac{\pi}{\mathrm{2}} \\ $$

Question Number 94239    Answers: 1   Comments: 0

x^2 (dy/dx) = x^2 +xy+y^2

$$\mathrm{x}^{\mathrm{2}} \:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 94237    Answers: 1   Comments: 1

Question Number 94243    Answers: 0   Comments: 3

By using the double integral find the area of the regiin bounded by the curve y=x^2 +2x , y=x^2 −2x and x−axis (sketch the region of integration) pleas sir help me

$${By}\:{using}\:{the}\:{double}\:{integral}\:{find}\:{the}\:{area}\:{of}\:{the}\:{regiin}\: \\ $$$${bounded}\:{by}\:{the}\:{curve}\:{y}={x}^{\mathrm{2}} +\mathrm{2}{x}\:,\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\:{x}−{axis}\: \\ $$$$\left({sketch}\:{the}\:{region}\:{of}\:{integration}\right) \\ $$$${pleas}\:{sir}\:{help}\:{me}\: \\ $$

Question Number 94220    Answers: 0   Comments: 5

∫x^x dx=?

$$\int\mathrm{x}^{\mathrm{x}} \mathrm{dx}=? \\ $$

Question Number 94219    Answers: 1   Comments: 1

∫x^x^x dx=?

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \mathrm{dx}=? \\ $$

Question Number 94214    Answers: 0   Comments: 4

Find f(0) when a polynomial f(x) satisfies lim_(x→1) ((f(x))/(x^2 −1))=2 lim_(x→−1) ((f(x))/(x^2 −1))=2 lim_(x→+∞) ((f(x))/x^4 ) =1 pls Help!

$${Find}\:{f}\left(\mathrm{0}\right)\:{when}\:{a}\:{polynomial}\:{f}\left({x}\right)\:{satisfies} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}=\mathrm{2} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\:\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}=\mathrm{2}\:\: \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\:\frac{{f}\left({x}\right)}{{x}^{\mathrm{4}} }\:=\mathrm{1}\:\:\:\:\:\:\:\:{pls}\:{Help}! \\ $$

Question Number 94212    Answers: 1   Comments: 0

Question Number 94201    Answers: 1   Comments: 1

Question Number 94210    Answers: 1   Comments: 0

((s(t+Δt)−s(t))/(Δt))

$$\frac{{s}\left({t}+\Delta{t}\right)−{s}\left({t}\right)}{\Delta{t}} \\ $$

Question Number 94193    Answers: 0   Comments: 5

Question Number 94191    Answers: 1   Comments: 0

Question Number 94186    Answers: 0   Comments: 1

∫(√(tan x)) dx=?

$$\int\sqrt{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}=? \\ $$

Question Number 94184    Answers: 4   Comments: 1

∫((x((x−a))^(1/3) )/((x−b))^(1/3) )dx=? ∫(((x−a))^(1/3) /(x((x−b))^(1/3) ))dx=?

$$\int\frac{{x}\sqrt[{\mathrm{3}}]{{x}−{a}}}{\sqrt[{\mathrm{3}}]{{x}−{b}}}{dx}=? \\ $$$$\int\frac{\sqrt[{\mathrm{3}}]{{x}−{a}}}{{x}\sqrt[{\mathrm{3}}]{{x}−{b}}}{dx}=? \\ $$

Question Number 94174    Answers: 1   Comments: 3

{ ((x+y = 10)),(((x)^(1/(3 )) + (y)^(1/(3 )) = (5/2) ((xy))^(1/(6 )) )) :} find x &y??

$$\begin{cases}{\mathrm{x}+\mathrm{y}\:=\:\mathrm{10}}\\{\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{y}}\:=\:\frac{\mathrm{5}}{\mathrm{2}}\:\sqrt[{\mathrm{6}\:\:}]{\mathrm{xy}}}\end{cases}\: \\ $$$$\mathrm{find}\:\mathrm{x}\:\&\mathrm{y}?? \\ $$

Question Number 94161    Answers: 1   Comments: 2

∫ (dx/(p+(√(qx+r))))

$$\int\:\frac{\mathrm{dx}}{\mathrm{p}+\sqrt{\mathrm{qx}+\mathrm{r}}}\: \\ $$

Question Number 94158    Answers: 0   Comments: 3

Question Number 94148    Answers: 0   Comments: 0

solve cosz =e^z zfrom C

$${solve}\:{cosz}\:={e}^{{z}} \:\:\:\:\:{zfrom}\:{C} \\ $$

Question Number 94144    Answers: 0   Comments: 2

There is a moving point P in a triangle ABC of which sides are a,b,c and a>b>c find the minimum and maximum of AP+BP+CP

$${There}\:{is}\:{a}\:{moving}\:{point}\:{P}\:{in}\:{a}\:{triangle} \\ $$$$\:{ABC}\:{of}\:{which}\:{sides}\:{are}\:{a},{b},{c}\:{and}\:{a}>{b}>{c} \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum} \\ $$$${of}\:{AP}+{BP}+{CP} \\ $$

Question Number 94143    Answers: 1   Comments: 3

∫ (dx/((x+(√(1+x^2 )))^2 )) =

$$\int\:\frac{{dx}}{\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:= \\ $$

Question Number 94135    Answers: 0   Comments: 2

f(x) is a continuous function forall real values of x and satisfies∫_0 ^x f(t).dt=∫_x ^1 t^2 .f(t).dt+(x^(16) /8)+(x^6 /3)+A Find A?

$${f}\left({x}\right)\:{is}\:{a}\:{continuous}\:{function}\:{forall}\:{real}\:{values}\:{of}\:{x}\:{and}\:{satisfies}\int_{\mathrm{0}} ^{{x}} {f}\left({t}\right).{dt}=\int_{{x}} ^{\mathrm{1}} {t}^{\mathrm{2}} .{f}\left({t}\right).{dt}+\frac{{x}^{\mathrm{16}} }{\mathrm{8}}+\frac{{x}^{\mathrm{6}} }{\mathrm{3}}+{A} \\ $$$${Find}\:{A}? \\ $$

Question Number 94134    Answers: 0   Comments: 1

lim_(x→1) ( (1/(x−1)) − (x/(ln x)) ) = ... ( Without L′ Hospital )

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\left(\:\frac{\mathrm{1}}{{x}−\mathrm{1}}\:−\:\frac{{x}}{\mathrm{ln}\:{x}}\:\right)\:=\:... \\ $$$$\left(\:{Without}\:\:{L}'\:{Hospital}\:\right) \\ $$

Question Number 94108    Answers: 0   Comments: 0

Question Number 94084    Answers: 0   Comments: 2

∫(√(cotx))dx

$$\int\sqrt{\mathrm{cot}{x}}{dx}\: \\ $$

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