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Question Number 203565 Answers: 1 Comments: 0

Solve the following equation simultaneously and find the stationary points: 2xy^2 c^2 − 4x^3 y^2 − 2xy^4 = 0 -----(1) 2x^2 yc^2 − 2x^4 y − 4x^2 y^3 = 0 -----(2) Please, I need a well detail calculation Thank you

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation}\:\mathrm{simultaneously} \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{stationary}\:\mathrm{points}: \\ $$$$\mathrm{2xy}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} \:−\:\mathrm{4x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} \:−\:\mathrm{2xy}^{\mathrm{4}} \:=\:\mathrm{0}\:-----\left(\mathrm{1}\right) \\ $$$$\mathrm{2x}^{\mathrm{2}} \mathrm{yc}^{\mathrm{2}} \:−\:\mathrm{2x}^{\mathrm{4}} \mathrm{y}\:−\:\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}} \:=\:\mathrm{0}\:-----\left(\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Please},\:\mathrm{I}\:\mathrm{need}\:\mathrm{a}\:\mathrm{well}\:\mathrm{detail}\:\mathrm{calculation} \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 203564 Answers: 1 Comments: 0

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

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

Question Number 203560 Answers: 0 Comments: 1

Question Number 203561 Answers: 0 Comments: 1

(√(2x−5+3=?))

$$\sqrt{\mathrm{2}{x}−\mathrm{5}+\mathrm{3}=?} \\ $$

Question Number 203557 Answers: 1 Comments: 1

Question Number 203554 Answers: 0 Comments: 0

Question Number 203547 Answers: 0 Comments: 0

Question Number 203545 Answers: 1 Comments: 0

If A,B,C are finite sets whose elements are from the same universal set U and n(A) denotes the number of element in the set A (a) Show by means of venn diagram that n(A ∪ B) = n(A) + n(B) − n(A ∩ B) (b) Using the fact that (A ∪ B ∪ C) = (A∪B)∪C =A∪(B∪C) deduce an expression for (A∪B∪C) (c) If n(A∪B)= n(A∩B), what can be said about A and B? How did you reach your conclusion. Thank you in advance

$$\mathrm{If}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{are}\:\mathrm{finite}\:\mathrm{sets}\:\mathrm{whose}\:\mathrm{elements}\:\mathrm{are}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{same}\:\mathrm{universal}\:\mathrm{set}\:\mathrm{U}\:\mathrm{and}\:\mathrm{n}\left(\mathrm{A}\right)\: \\ $$$$\mathrm{denotes}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set}\:\mathrm{A} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Show}\:\mathrm{by}\:\mathrm{means}\:\mathrm{of}\:\mathrm{venn}\:\mathrm{diagram}\:\mathrm{that} \\ $$$$\mathrm{n}\left(\mathrm{A}\:\cup\:\mathrm{B}\right)\:=\:\mathrm{n}\left(\mathrm{A}\right)\:+\:\mathrm{n}\left(\mathrm{B}\right)\:−\:\mathrm{n}\left(\mathrm{A}\:\cap\:\mathrm{B}\right) \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Using}\:\mathrm{the}\:\mathrm{fact}\:\mathrm{that}\:\left(\mathrm{A}\:\cup\:\mathrm{B}\:\cup\:\mathrm{C}\right)\:=\:\left(\mathrm{A}\cup\mathrm{B}\right)\cup\mathrm{C} \\ $$$$=\mathrm{A}\cup\left(\mathrm{B}\cup\mathrm{C}\right)\:\mathrm{deduce}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{for} \\ $$$$\left(\mathrm{A}\cup\mathrm{B}\cup\mathrm{C}\right) \\ $$$$\left(\mathrm{c}\right)\:\mathrm{If}\:\mathrm{n}\left(\mathrm{A}\cup\mathrm{B}\right)=\:\mathrm{n}\left(\mathrm{A}\cap\mathrm{B}\right),\:\:\mathrm{what}\:\mathrm{can}\:\mathrm{be}\:\mathrm{said} \\ $$$$\mathrm{about}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}?\:\mathrm{How}\:\mathrm{did}\:\mathrm{you}\:\mathrm{reach}\:\mathrm{your}\:\mathrm{conclusion}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance} \\ $$

Question Number 203544 Answers: 1 Comments: 0

∫_0 ^1_ (dx/((1−x^6 )^(1/6) )) =(π/3)

$$\int_{\mathrm{0}} ^{\mathrm{1}_{} } \frac{{dx}}{\left(\mathrm{1}−{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} }\:=\frac{\pi}{\mathrm{3}} \\ $$

Question Number 203533 Answers: 2 Comments: 0

Solve for x : 3^(x+2) =15^(x−1)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{2}} =\mathrm{15}^{\mathrm{x}−\mathrm{1}} \\ $$

Question Number 203529 Answers: 0 Comments: 0

Question Number 203527 Answers: 2 Comments: 0

Find the maximum value of the function f(x,y)=x^2 y^2 z^2 subject to the condition that x^2 +y^2 +z^2 =c^2 , where c is the constant. Thank you in advance

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} \mathrm{z}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} ,\:\mathrm{where}\:\mathrm{c}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}. \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance} \\ $$

Question Number 203526 Answers: 2 Comments: 0

Determine the maximum and minimum of the function: f(x,y)=x^4 +4x^2 y^2 −2x^2 +2y^2 −1 Thank you

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{function}: \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{2y}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 203525 Answers: 1 Comments: 0

Solve: 4x^3 +8xy^2 −4x=0 -----(1) 8x^2 y−4y =0 -----(2) simultaneosly i.e find the stationary point Thank you

$$\mathrm{Solve}:\: \\ $$$$\mathrm{4x}^{\mathrm{3}} +\mathrm{8xy}^{\mathrm{2}} −\mathrm{4x}=\mathrm{0}\:-----\left(\mathrm{1}\right) \\ $$$$\mathrm{8x}^{\mathrm{2}} \mathrm{y}−\mathrm{4y}\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:-----\left(\mathrm{2}\right) \\ $$$$\mathrm{simultaneosly}\:\mathrm{i}.\mathrm{e}\:\mathrm{find}\:\mathrm{the}\:\mathrm{stationary}\:\mathrm{point} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 203509 Answers: 0 Comments: 0

Find the value of: Π_(n=1) ^∞ ((2^n +1)/(2^n −1))

$${Find}\:{the}\:{value}\:{of}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{2}^{{n}} +\mathrm{1}}{\mathrm{2}^{{n}} −\mathrm{1}} \\ $$

Question Number 203508 Answers: 1 Comments: 0

Evaluate the given limit: lim_(n→∞) (((8)^(1/n) −1)/( ((16))^(1/n) −1))