Question and Answers Forum

AllQuestion and Answers: Page 500

Question Number 169346 Answers: 0 Comments: 0

Show that substituting y=vx, x+y(dy/dx)=x(dy/dx)−y to a separable equation for v and x and its solution is log_e (x^2 +y^2 )=2tan^(−1) ((y/x)) +C Mastermind

$${Show}\:{that}\:{substituting}\:{y}={vx}, \\ $$$${x}+{y}\frac{{dy}}{{dx}}={x}\frac{{dy}}{{dx}}−{y}\:{to}\:{a}\:{separable} \\ $$$${equation}\:{for}\:{v}\:{and}\:{x}\:{and}\:{its}\: \\ $$$${solution}\:{is}\:{log}_{{e}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)=\mathrm{2}{tan}^{−\mathrm{1}} \left(\frac{{y}}{{x}}\right) \\ $$$$+{C} \\ $$$$ \\ $$$${Mastermind} \\ $$$$\: \\ $$

Question Number 169342 Answers: 1 Comments: 0

Obtain the differential equation associated with the primitive y = Ae^(2x) +Be^x +C Mastermind

$${Obtain}\:{the}\:{differential}\:{equation} \\ $$$${associated}\:{with}\:{the}\:{primitive} \\ $$$${y}\:=\:{Ae}^{\mathrm{2}{x}} +{Be}^{{x}} +{C} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169340 Answers: 0 Comments: 0

Question Number 169432 Answers: 1 Comments: 0

n(A)=7 n(A∩B)=4 3n(A−B)=n(B) n(B−A)=?

$${n}\left({A}\right)=\mathrm{7} \\ $$$${n}\left({A}\cap{B}\right)=\mathrm{4} \\ $$$$\mathrm{3}{n}\left({A}−{B}\right)={n}\left({B}\right) \\ $$$${n}\left({B}−{A}\right)=? \\ $$

Question Number 169333 Answers: 0 Comments: 3

Show that if y=C_1 sinx + C_2 x then (1+xcotx)(d^2 y/dx^2 )−x(dy/dx)+y=0 Mastermind

$${Show}\:{that}\:{if}\:{y}={C}_{\mathrm{1}} {sinx}\:+\:{C}_{\mathrm{2}} {x}\:{then} \\ $$$$\left(\mathrm{1}+{xcotx}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−{x}\frac{{dy}}{{dx}}+{y}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169319 Answers: 1 Comments: 2

if f(2x−1)=x^2 −3x+2, find f(2)

$$\mathrm{if}\:\mathrm{f}\left(\mathrm{2x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{2},\:\:\mathrm{find}\:\mathrm{f}\left(\mathrm{2}\right) \\ $$

Question Number 169317 Answers: 2 Comments: 3

Question Number 169315 Answers: 1 Comments: 1

lim_(x→∞) (((1+(√(x+2)))/(1−(√(x+2))))) Mastermind

$${lim}_{{x}\rightarrow\infty} \left(\frac{\mathrm{1}+\sqrt{{x}+\mathrm{2}}}{\mathrm{1}−\sqrt{{x}+\mathrm{2}}}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169308 Answers: 0 Comments: 0

Question Number 169305 Answers: 4 Comments: 2

Differentiate the following wrt x 1) y=x^x 2) y=sin^(−1) (2x+1) Mastermind

$${Differentiate}\:{the}\:{following}\:{wrt}\:{x} \\ $$$$\left.\mathrm{1}\right)\:{y}={x}^{{x}} \\ $$$$\left.\mathrm{2}\right)\:{y}={sin}^{−\mathrm{1}} \left(\mathrm{2}{x}+\mathrm{1}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169304 Answers: 1 Comments: 4

3^x =4 4^y =12 ^(faind value of (((x+1)/(2xy)))=?)

$$\mathrm{3}^{{x}} =\mathrm{4} \\ $$$$\mathrm{4}^{{y}} =\mathrm{12}\:\:\:\:\:\overset{{faind}\:{value}\:{of}\:\left(\frac{{x}+\mathrm{1}}{\mathrm{2}{xy}}\right)=?} {\:} \\ $$

Question Number 169303 Answers: 1 Comments: 1

Given that: x cos y=sin(x+y), find (dy/dx) Mastermind

$${Given}\:{that}: \\ $$$${x}\:{cos}\:{y}={sin}\left({x}+{y}\right),\:{find}\:\frac{{dy}}{{dx}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169295 Answers: 0 Comments: 0

Prove without using Mathematical Induction that: cos^n x=(1/2^(n−1) )Σ_(k=0) ^((n−1)/2) C_k ^n cos (n−2k)x where x is any real number and n is any positive odd integer.

$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{using}\:\mathrm{Mathematical}\: \\ $$$$\mathrm{Induction}\:\mathrm{that}: \\ $$$$\mathrm{cos}^{{n}} {x}=\frac{\mathrm{1}}{\mathrm{2}^{{n}−\mathrm{1}} }\underset{{k}=\mathrm{0}} {\overset{\left({n}−\mathrm{1}\right)/\mathrm{2}} {\sum}}{C}_{{k}} ^{{n}} \mathrm{cos}\:\left({n}−\mathrm{2}{k}\right){x}\: \\ $$$$\mathrm{where}\:\:{x}\:\mathrm{is}\:\mathrm{any}\:\mathrm{real}\:\mathrm{number}\:\mathrm{and}\:{n}\:\mathrm{is}\:\mathrm{any} \\ $$$$\mathrm{positive}\:\mathrm{odd}\:\mathrm{integer}. \\ $$

Question Number 169294 Answers: 1 Comments: 2