Question and Answers Forum

AllQuestion and Answers: Page 1966

Question Number 11395 Answers: 0 Comments: 1

Prove that those functions below don′t have limit a) lim_((x,y)→(0,0)) ((xy)/(x^2 + y^2 )) b) lim_((x,y)→(0,0)) ((xy + y^3 )/(x^2 + y^2 ))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{those}\:\mathrm{functions}\:\mathrm{below}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{limit} \\ $$$$\left.\mathrm{a}\right)\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}}{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.{b}\right)\:\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}\:+\:{y}^{\mathrm{3}} }{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$

Question Number 11394 Answers: 0 Comments: 0

Find equation of the hyperbolas that intersect 3x^2 −4y^2 =5xy and 3y^2 −4x^2 =2x+5.

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolas}\:\mathrm{that}\: \\ $$$$\mathrm{intersect}\:\mathrm{3x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} =\mathrm{5xy}\:\mathrm{and}\: \\ $$$$\mathrm{3y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}. \\ $$

Question Number 11393 Answers: 0 Comments: 0

Question Number 11389 Answers: 1 Comments: 0

Given that the mean relative atomic mass of chlorine contain two isotopes of mass numbe 35 and 37. What is the percentage of composition of the isotope of mass number 37

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{relative}\:\mathrm{atomic}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{chlorine}\:\mathrm{contain}\:\mathrm{two}\:\mathrm{isotopes} \\ $$$$\mathrm{of}\:\mathrm{mass}\:\mathrm{numbe}\:\mathrm{35}\:\mathrm{and}\:\mathrm{37}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{composition}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{isotope}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{number}\:\mathrm{37}\: \\ $$

Question Number 11384 Answers: 1 Comments: 0

Out of 5 accountants and 7 bankers, a committee consisting of 2 accountants and 3 bankers is to be formed. In how many ways can this be done if (a) Any acountant and any bankers must be included (b) One particular banker must be included (c) 2 accountant cannot be in the committee

$$\mathrm{Out}\:\mathrm{of}\:\mathrm{5}\:\mathrm{accountants}\:\mathrm{and}\:\mathrm{7}\:\mathrm{bankers},\:\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of}\: \\ $$$$\mathrm{2}\:\mathrm{accountants}\:\mathrm{and}\:\mathrm{3}\:\mathrm{bankers}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this} \\ $$$$\mathrm{be}\:\mathrm{done}\:\mathrm{if} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Any}\:\mathrm{acountant}\:\mathrm{and}\:\mathrm{any}\:\mathrm{bankers}\:\mathrm{must}\:\mathrm{be}\:\mathrm{included} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{One}\:\mathrm{particular}\:\mathrm{banker}\:\mathrm{must}\:\mathrm{be}\:\mathrm{included} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{2}\:\mathrm{accountant}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{in}\:\mathrm{the}\:\mathrm{committee} \\ $$

Question Number 11383 Answers: 1 Comments: 0

There are six trains travelling between Abuja and Lagos and back. In how many ways can a man travel from abuja to Lagos by one train and return by a different train

$$\mathrm{There}\:\mathrm{are}\:\mathrm{six}\:\mathrm{trains}\:\mathrm{travelling}\:\mathrm{between}\:\mathrm{Abuja}\:\mathrm{and}\:\mathrm{Lagos}\:\mathrm{and}\:\mathrm{back}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{a}\:\mathrm{man}\:\mathrm{travel}\:\mathrm{from}\:\mathrm{abuja}\:\mathrm{to}\:\mathrm{Lagos}\:\mathrm{by}\:\mathrm{one}\:\mathrm{train}\:\mathrm{and} \\ $$$$\mathrm{return}\:\mathrm{by}\:\mathrm{a}\:\mathrm{different}\:\mathrm{train} \\ $$

Question Number 11382 Answers: 0 Comments: 2

In how many ways can 24 different articles be divided into groups of 12, 8 and 4 articles respectively

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{24}\:\mathrm{different}\:\mathrm{articles}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups}\:\mathrm{of} \\ $$$$\mathrm{12},\:\mathrm{8}\:\mathrm{and}\:\mathrm{4}\:\mathrm{articles}\:\mathrm{respectively} \\ $$

Question Number 11373 Answers: 1 Comments: 0

Question Number 11372 Answers: 0 Comments: 0

If G_1 and G_2 are groups , and f : G_1 →G_2 is a group homomorphism , then prove that o(G_1 ) = o(G_2 ) .

$$\mathrm{If}\:\mathrm{G}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{G}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{groups}\:,\:\mathrm{and}\:\mathrm{f}\::\:\mathrm{G}_{\mathrm{1}} \:\rightarrow\mathrm{G}_{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorphism}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{o}\left(\mathrm{G}_{\mathrm{1}} \right)\:=\:\mathrm{o}\left(\mathrm{G}_{\mathrm{2}} \right)\:. \\ $$

Question Number 11365 Answers: 0 Comments: 1

∅(n)=n−1 , n∈Z ,where ∅ is Eular phi function. True or false .And explain it .

$$\emptyset\left(\mathrm{n}\right)=\mathrm{n}−\mathrm{1}\:,\:\mathrm{n}\in\mathrm{Z}\:,\mathrm{where}\:\emptyset\:\mathrm{is}\:\mathrm{Eular}\:\mathrm{phi}\:\mathrm{function}. \\ $$$$\mathrm{True}\:\mathrm{or}\:\mathrm{false}\:.\mathrm{And}\:\mathrm{explain}\:\mathrm{it}\:. \\ $$

Question Number 11364 Answers: 1 Comments: 0

lim_(x→0) (((√(1 + tan x)) − (√(1 + sin x)))/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\sqrt{\mathrm{1}\:+\:\mathrm{tan}\:{x}}\:−\:\sqrt{\mathrm{1}\:+\:\mathrm{sin}\:{x}}}{{x}^{\mathrm{3}} } \\ $$

Question Number 11363 Answers: 0 Comments: 0

x∈Z f(x)=log_3 (((x−5)/(x−2)))⇒Σx=?

$$\mathrm{x}\in\mathrm{Z} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}_{\mathrm{3}} \left(\frac{\mathrm{x}−\mathrm{5}}{\mathrm{x}−\mathrm{2}}\right)\Rightarrow\Sigma\mathrm{x}=? \\ $$

Question Number 11356 Answers: 1 Comments: 0

Question Number 11355 Answers: 1 Comments: 0

z+3−2i=(1+i)×z^− ⇒∣z∣=?

$$\mathrm{z}+\mathrm{3}−\mathrm{2i}=\left(\mathrm{1}+\mathrm{i}\right)×\overset{−} {\mathrm{z}}\:\Rightarrow\mid\mathrm{z}\mid=? \\ $$

Question Number 11353 Answers: 0 Comments: 0

reduce the matrix below to echelon form and then to row canonical form A = [((2 4 2 −2 5 1)),((3 6 2 2 0 4)),((4 8 2 6 −5 7)) ]

$$\mathrm{reduce}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{below}\:\mathrm{to}\:\mathrm{echelon}\:\mathrm{form}\:\mathrm{and}\:\mathrm{then}\:\mathrm{to}\:\mathrm{row}\:\mathrm{canonical}\:\mathrm{form} \\ $$$$\mathrm{A}\:=\:\begin{bmatrix}{\mathrm{2}\:\:\mathrm{4}\:\:\mathrm{2}\:\:−\mathrm{2}\:\:\mathrm{5}\:\:\mathrm{1}}\\{\mathrm{3}\:\:\mathrm{6}\:\:\mathrm{2}\:\:\:\:\:\mathrm{2}\:\:\mathrm{0}\:\:\mathrm{4}}\\{\mathrm{4}\:\:\mathrm{8}\:\:\mathrm{2}\:\:\:\mathrm{6}\:\:−\mathrm{5}\:\mathrm{7}}\end{bmatrix} \\ $$

Question Number 11352 Answers: 1 Comments: 0

if, A = x^2 sin yi + z^2 cos yj − xy^2 k, find, dA

$$\mathrm{if},\:\:\mathrm{A}\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\:\mathrm{yi}\:+\:\mathrm{z}^{\mathrm{2}} \:\mathrm{cos}\:\mathrm{yj}\:−\:\mathrm{xy}^{\mathrm{2}} \mathrm{k},\:\:\mathrm{find},\:\:\mathrm{dA}\:\: \\ $$

Question Number 11388 Answers: 0 Comments: 0

A cell supplies a current of 6 ameter through a 2 coil and a current of 0.2 ameter through 7 coil. Calculate the limits and the internal resistance of the cell

$$\mathrm{A}\:\mathrm{cell}\:\mathrm{supplies}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{6}\:\mathrm{ameter}\:\mathrm{through}\:\mathrm{a}\:\mathrm{2}\:\mathrm{coil}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\: \\ $$$$\mathrm{ameter}\:\mathrm{through}\:\mathrm{7}\:\mathrm{coil}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{and}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{resistance} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{cell} \\ $$

Question Number 11351 Answers: 0 Comments: 0

Find the workdone in moving a paticle once around an ellipse C in the xy plane. if the ellipse has centre at the origin with semi major and semi minor axes 4 and 3 respectively.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{workdone}\:\mathrm{in}\:\mathrm{moving}\:\mathrm{a}\:\mathrm{paticle}\:\mathrm{once}\:\mathrm{around}\:\mathrm{an}\:\mathrm{ellipse}\:\mathrm{C}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{xy}\:\mathrm{plane}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{ellipse}\:\mathrm{has}\:\mathrm{centre}\:\mathrm{at}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{with}\:\mathrm{semi}\:\mathrm{major}\:\mathrm{and}\:\mathrm{semi}\:\mathrm{minor}\:\mathrm{axes}\: \\ $$$$\mathrm{4}\:\mathrm{and}\:\mathrm{3}\:\mathrm{respectively}. \\ $$

Question Number 11344 Answers: 0 Comments: 1

n_c_n =((n!)/((n−n)!n!))

$${n}_{{c}_{{n}} } =\frac{{n}!}{\left({n}−{n}\right)!{n}!} \\ $$

Question Number 11343 Answers: 0 Comments: 1

n_c_n =((n1)/((n−n)))

$${n}_{\boldsymbol{\mathrm{c}}_{\boldsymbol{\mathrm{n}}} } =\frac{{n}\mathrm{1}}{\left({n}−{n}\right)} \\ $$

Question Number 11341 Answers: 0 Comments: 2