Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x squared minus x end fraction minus fraction numerator x minus 1 over denominator x cubed minus 3 x squared plus 2 x end fraction close square brackets

  1. 1
  2. 2
  3. 0
  4. 1 half

hintHint:

We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x squared minus x end fraction minus fraction numerator x minus 1 over denominator x cubed minus 3 x squared plus 2 x end fraction close square brackets.

The correct answer is: 2


    Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x squared minus x end fraction minus fraction numerator x minus 1 over denominator x cubed minus 3 x squared plus 2 x end fraction close square brackets
    If we put x=1 in the given Function, we get 0 over 0.
    Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x squared minus x end fraction minus fraction numerator x minus 1 over denominator x cubed minus 3 x squared plus 2 x end fraction close square brackets = Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator 1 minus 1 over denominator 1 squared minus 1 end fraction minus fraction numerator 1 minus 1 over denominator 1 cubed minus 3 cross times 1 squared plus 2 cross times 1 end fraction close square brackets = 0 over 0
    So, We can write,
    Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x squared minus x end fraction close square brackets - Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator x minus 1 over denominator x cubed minus 3 x squared plus 2 x end fraction close square brackets
    Factorizing Numerator and Denominator.
    x to the power of 2 space end exponent minus x space equals x left parenthesis x minus 1 right parenthesis
x cubed minus 3 x squared plus 2 x space equals space x left parenthesis x space minus 1 right parenthesis left parenthesis x minus 2 right parenthesis
    or, Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets 1 over x close square brackets - Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator 1 over denominator x left parenthesis x minus 2 right parenthesis end fraction close square brackets
    or, Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets 1 over x close square brackets-Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets 1 over x close square brackets-Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator 1 over denominator x minus 2 end fraction close square brackets
    or, - Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator 1 over denominator x minus 2 end fraction close square brackets
    On substituting, We get
     - Lt subscript x not stretchy rightwards arrow 1 end subscript space open square brackets fraction numerator 1 over denominator x minus 2 end fraction close square brackets =1

    We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

    Related Questions to study

    General
    Maths-

    L t subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 6 x squared plus 9 x over denominator x squared minus 9 end fraction

    We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means fraction numerator 0 over denominator 0 space end fraction space o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

    L t subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 6 x squared plus 9 x over denominator x squared minus 9 end fraction

    Maths-General

    We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means fraction numerator 0 over denominator 0 space end fraction space o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.

    General
    physics-

    The graph shown in the adjacent diagram, represents the variation of temperature T of two bodies x and y having same surface area, with time (t) due to emission of radiation. Find the correct relation between emissive power(E) and absorptive power(a) of the two bodies

    The graph shown in the adjacent diagram, represents the variation of temperature T of two bodies x and y having same surface area, with time (t) due to emission of radiation. Find the correct relation between emissive power(E) and absorptive power(a) of the two bodies

    physics-General
    General
    physics-

    Two circular disc A and B with equal radii are blackened. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves (R is rate of cooling)

    Two circular disc A and B with equal radii are blackened. They are heated to same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves (R is rate of cooling)

    physics-General
    parallel
    General
    physics-

    A block of steel heated to 100degreeC is left in a room to cool. Which of the curves shown in the figure, represents the correct behaviour

    A block of steel heated to 100degreeC is left in a room to cool. Which of the curves shown in the figure, represents the correct behaviour

    physics-General
    General
    physics-

    Cooling graphs are drawn for three liquids a,b and c The specific heat is maximum for liquid

    Cooling graphs are drawn for three liquids a,b and c The specific heat is maximum for liquid

    physics-General
    General
    physics-

    Absorptive power of a white body and of a perfectly black body respectively are

    Absorptive power of a white body and of a perfectly black body respectively are

    physics-General
    parallel
    General
    chemistry-

    The energies E1 and E2 of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e. λ and λ will be:

    The energies E1 and E2 of two radiations are 25 eV and 50 eV respectively. The relation between their wavelengths i.e. λ and λ will be:

    chemistry-General
    General
    chemistry-

    The first Lyman transition in the hydrogen spectrum has ΔE =10.2 eV. The same energy change is observed in the second Balmer transition of -

    The first Lyman transition in the hydrogen spectrum has ΔE =10.2 eV. The same energy change is observed in the second Balmer transition of -

    chemistry-General
    General
    chemistry-

    Which of the following substance will have highest b.p.t.?

    Which of the following substance will have highest b.p.t.?

    chemistry-General
    parallel
    General
    chemistry-

    Which of the followinhas the lowesmelting point-

    Which of the followinhas the lowesmelting point-

    chemistry-General
    General
    chemistry-

    The electronic structurof four elements a,b,c and d are a=1s2,b =1s2,2s22p2,c =1s22s22p5,d=1s2 2s22p6 Thtendenctforelectrovalenbonis greatest in-

    The electronic structurof four elements a,b,c and d are a=1s2,b =1s2,2s22p2,c =1s22s22p5,d=1s2 2s22p6 Thtendenctforelectrovalenbonis greatest in-

    chemistry-General
    General
    chemistry-

    In whicothfollowinpaithboillinpoinof firscompouninot morthathsecond:

    In whicothfollowinpaithboillinpoinof firscompouninot morthathsecond:

    chemistry-General
    parallel
    General
    chemistry-

    Compound of a metal Mis M2O3. The formuloitnitridwilbe-

    Compound of a metal Mis M2O3. The formuloitnitridwilbe-

    chemistry-General
    General
    chemistry-

    The compound formed by which of the following pair of ions wilhave lowesmelting
    point:

    The compound formed by which of the following pair of ions wilhave lowesmelting
    point:

    chemistry-General
    General
    chemistry-

    Formula of a metal oxide is MOformula of its phosphate will be-

    Formula of a metal oxide is MOformula of its phosphate will be-

    chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.