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Find the points of discontinuity of y = ...

Find the points of discontinuity of `y = (1)/(u^(2) + u -2)`, where `u = (1)/(x -1)`

Text Solution

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The correct Answer is:
`x = (1)/(2), 1 and 2`
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Knowledge Check

  • Let f be a composite function of x defined by f (u) = (1)/( u ^(2) + u - 2) ' u (x) = (1)/( x -1). Then the number of points x where f is discontinuous is :

    A
    6
    B
    3
    C
    2
    D
    1

  • If x =u is a point of discontinuity of f(x)= lim_(n to oo) cos^(2n)x , then the value of cos u is

    A
    0
    B
    `1//2`
    C
    `(-1)^n`
    D
    1

  • If y = (u -1)/(u + 1) and u = sqrt(x) , then (dy)/(dx) is

    A
    `1/(sqrt(x)(1 + sqrt(x))^(2))`
    B
    `1/(sqrt(x)(1-sqrt(x))^(2))`
    C
    `1/(sqrt(x)(1 + sqrt(x))^(-2))`
    D
    `sqrt(x)(1 + sqrt(x))^(2)`

    • Similar Questions

    Explore conceptually related problems

    Discuss the continuity for f(x)=(1-u^(2))/(2+u^(2)) where u=sec x.

    For each of the following functions find the points of discontinuity and determine their character : (a) y=(1)/u^(2)+u-2," where u"=1/(x-1) .

    If y=(1)/(4)u^(4),u=(2)/(3)x^(3)+5 , then (dy)/(dx)=

    The function u_(n) takes on the following values : u_(1) = ( 1)/( 4) , u_(2) = ( 1)/( 4) + ( 1)/( 10)"…....." u_(n) =(1)/( 3+1) + ( 1)/( 3^(2) + 1)+"…........." (1)/( 3^(n) + 1)"…........." Prove that underset( n rarr oo) ( "lim") u_(a) lt (1)/(2)

    If x=sqrt (1+u^(2)),y =log (1+u^(2) ) ,then (dy)/(dx) =

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