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Question Number 25825    Answers: 1   Comments: 0

f:R→R is defined by f(x)={1_(−1 if x∉Z) if x∈Z Is f continuous at x=1 and x=−(3/2) ∫?

$${f}:{R}\rightarrow{R}\:{is}\:{defined}\:{by}\: \\ $$$${f}\left({x}\right)=\left\{\underset{−\mathrm{1}\:\:{if}\:{x}\notin{Z}} {\mathrm{1}}\:\:\:\mathrm{if}\:\mathrm{x}\in{Z}\right. \\ $$$${Is}\:{f}\:{continuous}\:{at}\:{x}=\mathrm{1}\:{and}\:{x}=−\frac{\mathrm{3}}{\mathrm{2}}\:\int? \\ $$$$ \\ $$

Question Number 25814    Answers: 1   Comments: 0

find δ>0 such that ∣f(x)+1∣<0.01 when 0<∣x−2∣<δ,where f(x)=((x^2 −5x+6)/(x−2)),hence use ε_δ definition to show that ((lim)/(xtends 2))f(x)=−1

$${find}\:\delta>\mathrm{0}\:{such}\:{that}\:\mid{f}\left({x}\right)+\mathrm{1}\mid<\mathrm{0}.\mathrm{01} \\ $$$${when}\:\mathrm{0}<\mid{x}−\mathrm{2}\mid<\delta,{where} \\ $$$${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{6}}{{x}−\mathrm{2}},{hence}\:{use}\:\varepsilon\_\delta\:\: \\ $$$${definition}\:{to}\:{show}\:{that}\: \\ $$$$\frac{{lim}}{{xtends}\:\mathrm{2}}{f}\left({x}\right)=−\mathrm{1} \\ $$

Question Number 25800    Answers: 2   Comments: 0

is sum of two periodic function is also periodic give reason

$${is}\:{sum}\:{of}\:{two}\:{periodic}\:{function}\:{is} \\ $$$${also}\:{periodic}\:{give}\:{reason} \\ $$

Question Number 25778    Answers: 1   Comments: 0

Question Number 25745    Answers: 1   Comments: 0

find the volume of the solid generated by thr revolution of the curve y(x^2 +a^2 )=a^3 about itd asymptote.

$${find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\: \\ $$$${generated}\:{by}\:{thr}\:{revolution}\:{of}\:{the} \\ $$$${curve}\:{y}\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)={a}^{\mathrm{3}} \:{about}\:{itd}\: \\ $$$${asymptote}. \\ $$

Question Number 25744    Answers: 1   Comments: 0

find the surface area of the solid formed by the rotation of the arc of the cycloid x=a(t+sin t), y=a(1+cost) about x axis

$${find}\:{the}\:{surface}\:{area}\:{of}\:{the}\:{solid}\: \\ $$$${formed}\:{by}\:{the}\:{rotation}\:{of}\:{the}\:{arc}\:{of}\: \\ $$$${the}\:{cycloid}\:{x}={a}\left({t}+{sin}\:{t}\right),\: \\ $$$${y}={a}\left(\mathrm{1}+{cost}\right)\:{about}\:{x}\:{axis} \\ $$

Question Number 25656    Answers: 0   Comments: 3

trace the curve y^2 (x+1)=x^2 (3−x) clearly stating all the properties used for tracing.

$${trace}\:{the}\:{curve}\: \\ $$$${y}^{\mathrm{2}} \left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \left(\mathrm{3}−{x}\right) \\ $$$${clearly}\:{stating}\:{all}\:{the}\:{properties}\:{used} \\ $$$${for}\:{tracing}. \\ $$

Question Number 25655    Answers: 0   Comments: 0

use lagranges mean value theorem to prove that x<sin^(−1) x<(x/(√(1−x^2 ))),0<x<1.

$${use}\:{lagranges}\:{mean}\:{value}\:{theorem}\:{to} \\ $$$${prove}\:{that}\: \\ $$$${x}<{sin}^{−\mathrm{1}} {x}<\frac{{x}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }},\mathrm{0}<{x}<\mathrm{1}. \\ $$

Question Number 25635    Answers: 0   Comments: 1

let f be the function defined on [−1,1] by f(x)={ { ((−1,if x is rational)),((1,if x is irrational.)) :} find U(P,f) and L(P,f).f is integrable or not ?

$${let}\:{f}\:{be}\:{the}\:{function}\:{defined}\:{on} \\ $$$$\left[−\mathrm{1},\mathrm{1}\right]\:{by} \\ $$$${f}\left({x}\right)=\left\{\begin{cases}{−\mathrm{1},{if}\:{x}\:{is}\:{rational}}\\{\mathrm{1},{if}\:{x}\:{is}\:{irrational}.}\end{cases}\right. \\ $$$${find}\:{U}\left({P},{f}\right)\:{and}\:{L}\left({P},{f}\right).{f}\:{is}\:{integrable} \\ $$$${or}\:{not}\:? \\ $$

Question Number 25634    Answers: 1   Comments: 0

find the equation of the tangent to the curve (√x)+(√y)=(√a) at any point (x,y)on it.

$${find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\: \\ $$$${the}\:{curve}\:\sqrt{{x}}+\sqrt{{y}}=\sqrt{{a}}\:{at}\:{any}\:{point} \\ $$$$\left({x},{y}\right){on}\:{it}. \\ $$

Question Number 25630    Answers: 1   Comments: 0

Question Number 25628    Answers: 0   Comments: 0

Question Number 25578    Answers: 0   Comments: 0

3 men A,B and C can complete a work in such a way that A works for all the days, B works for 1st and 2nd day and C works for 3rd, 4th and 5th day. If B and C can do as much work in two days as a alone does in 3 days. If B and C can complete the work without tbe help of A in 6 days then how many dahs A alone do the work?

$$\mathrm{3}\:\mathrm{men}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{a} \\ $$$$\mathrm{work}\:\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{A}\:\mathrm{works}\:\mathrm{for} \\ $$$$\mathrm{all}\:\mathrm{the}\:\mathrm{days},\:\mathrm{B}\:\mathrm{works}\:\mathrm{for}\:\mathrm{1st}\:\mathrm{and}\:\mathrm{2nd} \\ $$$$\mathrm{day}\:\mathrm{and}\:\mathrm{C}\:\mathrm{works}\:\mathrm{for}\:\mathrm{3rd},\:\mathrm{4th}\:\mathrm{and}\:\mathrm{5th} \\ $$$$\mathrm{day}.\:\mathrm{If}\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{can}\:\mathrm{do}\:\mathrm{as}\:\mathrm{much}\:\mathrm{work} \\ $$$$\mathrm{in}\:\mathrm{two}\:\mathrm{days}\:\mathrm{as}\:\mathrm{a}\:\mathrm{alone}\:\mathrm{does}\:\mathrm{in}\:\mathrm{3}\:\mathrm{days}. \\ $$$$\mathrm{If}\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{can}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\: \\ $$$$\mathrm{without}\:\mathrm{tbe}\:\mathrm{help}\:\mathrm{of}\:\mathrm{A}\:\mathrm{in}\:\mathrm{6}\:\mathrm{days}\:\mathrm{then}\: \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{dahs}\:\mathrm{A}\:\mathrm{alone}\:\mathrm{do}\:\mathrm{the}\:\mathrm{work}? \\ $$

Question Number 25569    Answers: 0   Comments: 8

if y =(sin^(−1) x)^2 ,check whether (1−x^2 )y_(n+2) −(2n+1)xy_(n+1) +n^2 y_n =0 or not.

$${if}\:{y}\:=\left({sin}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} ,{check}\:{whether} \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} −\left(\mathrm{2}{n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +{n}^{\mathrm{2}} {y}_{{n}} =\mathrm{0} \\ $$$${or}\:{not}. \\ $$

Question Number 25567    Answers: 2   Comments: 1

if y( sinx)^((sinx)^((sinx).^.^.^(.∞) ) ) find dy/dx.

$${if}\:{y}\left(\:{sinx}\right)^{\left({sinx}\right)^{\left({sinx}\right).^{.^{.^{.\infty} } } } } \\ $$$${find}\:{dy}/{dx}. \\ $$

Question Number 25509    Answers: 0   Comments: 1

Question Number 25736    Answers: 0   Comments: 0

Question Number 25483    Answers: 1   Comments: 0

valute ∫(1/((x−1)^2 ))(/((x^2 +4)))dx

$${valute}\:\int\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }\frac{}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx} \\ $$

Question Number 25476    Answers: 1   Comments: 0

convert 1234.24_8 to base 10

$${convert}\:\mathrm{1234}.\mathrm{24}_{\mathrm{8}} \:{to}\:{base}\:\mathrm{10} \\ $$

Question Number 25472    Answers: 1   Comments: 0

slolve the definite integral∫_1^ ^2 (1/x)dxusingg> ng trapezoidal rule with 4 sub intervals hencefind an approximate value of ln 2.

$${slolve}\:{the}\:{definite}\:{integral}\int_{\mathrm{1}^{} } ^{\mathrm{2}} \frac{\mathrm{1}}{{x}}{dxusingg}>\:\:\:{ng}\: \\ $$$${trapezoidal}\:{rule}\:{with}\:\mathrm{4}\:{sub}\:{intervals}\: \\ $$$${hencefind}\:{an}\:{approximate}\:{value}\:{of}\: \\ $$$${ln}\:\mathrm{2}. \\ $$

Question Number 25414    Answers: 1   Comments: 0

if 10^(10 ) electrons are removed neutral bodyb body the charge acquired by the body is? ?

$${if}\:\mathrm{10}^{\mathrm{10}\:} {electrons}\:{are}\:{removed}\:{neutral}\:{bodyb} \\ $$$${body}\:{the}\:{charge}\:{acquired}\:{by}\:{the}\:{body}\:{is}? \\ $$$$? \\ $$$$ \\ $$

Question Number 25410    Answers: 0   Comments: 0

Question Number 25780    Answers: 1   Comments: 0

every periodic function is differentiable.true or false justify

$${every}\:{periodic}\:{function}\:{is}\: \\ $$$${differentiable}.{true}\:{or}\:{false}\:{justify} \\ $$

Question Number 25275    Answers: 0   Comments: 0

Question Number 25103    Answers: 1   Comments: 0

Question Number 25091    Answers: 1   Comments: 0

A particle of mass m moving with speed u collides perfectly inelastically with a sphere of radius R and same mass, at rest, at an impact parameter d. Find (a) Angle between their final velocities (b) Magnitude of their final velocities

$${A}\:{particle}\:{of}\:{mass}\:{m}\:{moving}\:{with} \\ $$$${speed}\:{u}\:{collides}\:{perfectly}\:{inelastically} \\ $$$${with}\:{a}\:{sphere}\:{of}\:{radius}\:{R}\:{and}\:{same} \\ $$$${mass},\:{at}\:{rest},\:{at}\:{an}\:{impact}\:{parameter} \\ $$$${d}.\:{Find} \\ $$$$\left({a}\right)\:{Angle}\:{between}\:{their}\:{final}\:{velocities} \\ $$$$\left({b}\right)\:{Magnitude}\:{of}\:{their}\:{final} \\ $$$${velocities} \\ $$

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