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Question Number 96868 Answers: 0 Comments: 1

Question Number 96864 Answers: 2 Comments: 1

∫ (dy/(y^2 (5−y^2 ))) ?

$$\int\:\frac{\mathrm{dy}}{\mathrm{y}^{\mathrm{2}} \left(\mathrm{5}−\mathrm{y}^{\mathrm{2}} \right)}\:? \\ $$

Question Number 141856 Answers: 1 Comments: 0

Question Number 141855 Answers: 1 Comments: 0

Question Number 96848 Answers: 1 Comments: 0

Question Number 96846 Answers: 0 Comments: 1

Question Number 96845 Answers: 2 Comments: 0

If sin^(−1) (x/5) + cosec^(−1) (5/4) = (π/2), then x=

$$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{5}}\:+\:\mathrm{cosec}^{−\mathrm{1}} \frac{\mathrm{5}}{\mathrm{4}}\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then}\:{x}= \\ $$

Question Number 96839 Answers: 0 Comments: 0

Question Number 96837 Answers: 1 Comments: 0

determine f continue on [a,b] wich verify (∫_a ^b f(x)dx)^2 =∫_a ^b f^2 (x)dx

$$\mathrm{determine}\:\mathrm{f}\:\mathrm{continue}\:\mathrm{on}\:\left[\mathrm{a},\mathrm{b}\right]\:\mathrm{wich}\:\mathrm{verify}\:\left(\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)^{\mathrm{2}} \:=\int_{\mathrm{a}} ^{\mathrm{b}} \:\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 96836 Answers: 2 Comments: 0

a_n is a sequence wich verify a_(n+1) +a_n =(1/(n+1)) ∀n calculate Σ_(n=0) ^∞ a_n x^n

$$\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:\forall\mathrm{n} \\ $$$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \\ $$

Question Number 96834 Answers: 2 Comments: 1

1)calculate I_n = ∫_0 ^∞ (dx/((2x^2 +5x+3)^n )) 2) calculate ∫_0 ^∞ (dx/((2x^2 +5x+3)^2 )) and ∫_0 ^∞ (dx/((2x^2 +5x +3)^3 ))

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{I}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{3}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5x}\:+\mathrm{3}\right)^{\mathrm{3}} } \\ $$

Question Number 96829 Answers: 0 Comments: 1

If 2f(x) + f(1−x) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 96826 Answers: 1 Comments: 0

If 2f(x) + f(x−1) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:.\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$

Question Number 96823 Answers: 2 Comments: 2

Question Number 96821 Answers: 3 Comments: 0

{ (((u^2 /v) + (v^2 /u) = 12)),(((1/u) + (1/v) = (1/3))) :} . find u and v ?

$$\begin{cases}{\frac{\mathrm{u}^{\mathrm{2}} }{\mathrm{v}}\:+\:\frac{\mathrm{v}^{\mathrm{2}} }{\mathrm{u}}\:=\:\mathrm{12}}\\{\frac{\mathrm{1}}{\mathrm{u}}\:+\:\frac{\mathrm{1}}{\mathrm{v}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\end{cases}\:.\:\mathrm{find}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:? \\ $$

Question Number 96817 Answers: 1 Comments: 2

Question Number 96815 Answers: 1 Comments: 0

In how many ways can 3 boys and 3 girls be sitted in a line?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{3}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{3}\:\mathrm{girls}\:\mathrm{be} \\ $$$$\mathrm{sitted}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}? \\ $$

Question Number 96811 Answers: 1 Comments: 0

Prove that; a\ A+A∙B=A c\ (A+B^ )∙(A+B^− )=A b\ A∙(A+B)=A d\ A+A^− B=A+B

$$\mathrm{Prove}\:\mathrm{that}; \\ $$$$\mathrm{a}\backslash\:\mathrm{A}+\mathrm{A}\centerdot\mathrm{B}=\mathrm{A}\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\backslash\:\left(\mathrm{A}+\mathrm{B}^{} \right)\centerdot\left(\mathrm{A}+\overset{−} {\mathrm{B}}\right)=\mathrm{A} \\ $$$$\mathrm{b}\backslash\:\mathrm{A}\centerdot\left(\mathrm{A}+\mathrm{B}\right)=\mathrm{A}\:\:\:\:\:\:\:\mathrm{d}\backslash\:\mathrm{A}+\overset{−} {\mathrm{A}B}=\mathrm{A}+\mathrm{B} \\ $$

Question Number 96792 Answers: 1 Comments: 12

Question Number 96785 Answers: 1 Comments: 0

Question Number 96784 Answers: 1 Comments: 0

Question Number 96782 Answers: 3 Comments: 1

1)((cos^4 (θ))/x)−((sin^4 (θ))/y)=(1/(x+y)) find (dy/dx) 2)solve:2⌊x−4+⌊x⌋⌋=6−3⌊x⌋ 3)lim_(x→4) (((cos(x))^x −(sin(x))^x −cos(2x))/((x−4)))

$$\left.\mathrm{1}\right)\frac{{cos}^{\mathrm{4}} \left(\theta\right)}{{x}}−\frac{{sin}^{\mathrm{4}} \left(\theta\right)}{{y}}=\frac{\mathrm{1}}{{x}+{y}} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve}:\mathrm{2}\lfloor{x}−\mathrm{4}+\lfloor{x}\rfloor\rfloor=\mathrm{6}−\mathrm{3}\lfloor{x}\rfloor \\ $$$$ \\ $$$$\left.\mathrm{3}\right)\underset{{x}\rightarrow\mathrm{4}} {{lim}}\frac{\left({cos}\left({x}\right)\right)^{{x}} −\left({sin}\left({x}\right)\right)^{{x}} −{cos}\left(\mathrm{2}{x}\right)}{\left({x}−\mathrm{4}\right)} \\ $$$$ \\ $$$$ \\ $$

Question Number 96780 Answers: 0 Comments: 5

Question Number 96773 Answers: 1 Comments: 0

solve y^(′′) −y =((sinx)/x)

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{y}\:=\frac{\mathrm{sinx}}{\mathrm{x}} \\ $$

Question Number 96772 Answers: 2 Comments: 0

solve y^(′′) −2y =x^2 sinx and y(0)=0 ,y^′ (0) =1

$$\mathrm{solve}\:\mathrm{y}^{''} −\mathrm{2y}\:=\mathrm{x}^{\mathrm{2}} \mathrm{sinx}\:\:\mathrm{and}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:,\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\mathrm{1} \\ $$

Question Number 96771 Answers: 1 Comments: 0

solve y^(′′) −y^′ +y = cos(2t) with y(0)=y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2t}\right)\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

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