Maths-
General
Easy

Question

L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator square root of open parentheses 1 plus x plus x squared close parentheses end root minus 1 over denominator x end fraction

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

hintHint:

In the question first we will use the L hospital theorem, fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator f apostrophe open parentheses x close parentheses over denominator g apostrophe open parentheses x close parentheses end fraction. Then we will put the value of x.

The correct answer is: 1 half


    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator square root of open parentheses 1 plus x plus x squared close parentheses end root minus 1 over denominator x end fraction
    using L hospital theorem,
    equals limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator d square root of 1 plus x plus x squared end root over denominator d x end fraction end style minus begin display style fraction numerator d blank over denominator d x end fraction end style 1 over denominator begin display style fraction numerator d x over denominator d x end fraction end style end fraction
equals limit as x rightwards arrow 0 of fraction numerator 1 plus 2 x over denominator 2 square root of 1 plus x plus x squared end root end fraction
equals fraction numerator 1 plus 2 cross times 0 over denominator 2 square root of 1 plus 0 plus 0 end root end fraction
equals 1 half

    Related Questions to study

    General
    Maths-

    Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction

    Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction

    Maths-General
    General
    chemistry-

    Oxygen atom of ether is:

    Oxygen atom of ether is:

    chemistry-General
    General
    physics-

    A long current carrying wire, carrying current such that it is flowing out from the plane of paper, is placed at O A steady state current is flowing in the loop ABCD

    A long current carrying wire, carrying current such that it is flowing out from the plane of paper, is placed at O A steady state current is flowing in the loop ABCD

    physics-General
    parallel
    General
    physics-

    A loop carrying current I lies in the x-y plane as shown in fig The unit vector k^ is coming out of the plane of the paper The magnetic moment of the current loop is

    A loop carrying current I lies in the x-y plane as shown in fig The unit vector k^ is coming out of the plane of the paper The magnetic moment of the current loop is

    physics-General
    General
    physics-

    A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point such that

    A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point such that

    physics-General
    General
    physics-

    In figure, a particle is placed at the highest point A of a smooth sphere of radius r. It is given slight push, and it leaves the sphere at B, at a depth h vertically below A such that h is equal to

    In figure, a particle is placed at the highest point A of a smooth sphere of radius r. It is given slight push, and it leaves the sphere at B, at a depth h vertically below A such that h is equal to

    physics-General
    parallel
    General
    Maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of tan space x end exponent minus e to the power of x over denominator tan space x minus x end fraction

    Maths-General
    General
    Maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x times 2 to the power of x minus x over denominator 1 minus cos space x end fraction

    Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator x times 2 to the power of x minus x over denominator 1 minus cos space x end fraction

    Maths-General
    General
    chemistry-

    C-O-C angle would be maximum in

    C-O-C angle would be maximum in

    chemistry-General
    parallel
    General
    physics-

    A circular loop of radius 20cm is placed in a uniform magnetic field B=2T in X-Yplane the loop carries a current 1A in the direction shown in figure The magnitude of torque acting on the loop is nearly

    A circular loop of radius 20cm is placed in a uniform magnetic field B=2T in X-Yplane the loop carries a current 1A in the direction shown in figure The magnitude of torque acting on the loop is nearly

    physics-General
    General
    physics-

    Two 1ong wires are placed parallel to each other 10cm apart as shown in fig The magnetic field at piont P is

    Two 1ong wires are placed parallel to each other 10cm apart as shown in fig The magnetic field at piont P is

    physics-General
    General
    physics-

    A proton accelerated by a pd V=500 KV moves through a transverse magnetic field B=0.51 T as shown in figure Then the angle q through which the proton deviates from the initial direction of its motion is (approximately)

    A proton accelerated by a pd V=500 KV moves through a transverse magnetic field B=0.51 T as shown in figure Then the angle q through which the proton deviates from the initial direction of its motion is (approximately)

    physics-General
    parallel
    General
    physics-

    A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in fig Region II has a uniform magnetic field B perpendicular to the plane of the paper The length of the Region II is l Then

    A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in fig Region II has a uniform magnetic field B perpendicular to the plane of the paper The length of the Region II is l Then

    physics-General
    General
    physics-

    A small sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The force acting on the sphere are shown in figure. Which of the following statements is wrong?

    A small sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The force acting on the sphere are shown in figure. Which of the following statements is wrong?

    physics-General
    General
    Maths-

    L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction

    L t subscript x not stretchy rightwards arrow pi over 2 end subscript fraction numerator sec space x minus tan space x over denominator pi over 2 minus x end fraction

    Maths-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.