Maths-
General
Easy

Question

L t subscript left parenthesis x rightwards arrow 0 right parenthesis invisible function application left parenthesis t a n invisible function application x minus s i n invisible function application x right parenthesis divided by x squared equals

  1. 1
  2. space 1 divided by 2
  3. -1
  4. 0

hintHint:

We will apply L'Hôpital's Rule because we are getting open parentheses 0 over 0 close parentheses space f o r m and we will apply it till we don't get the value of the limit.

The correct answer is: 0


    In this question we have to find the limit of limit as x minus greater than 0 of fraction numerator tan open parentheses x close parentheses minus sin open parentheses x close parentheses over denominator x squared end fraction
    Step1: Putting the value of limit in expression
    By the value of straight x equals 0, both numerator and denominator become zero.open parentheses 0 over 0 close parentheses space f o r m .
    Step2: Taking the derivative of both numerator and denominator.
    According to L'Hôpital's Rule when we get open parentheses 0 over 0 close parentheses space f o r m we can differentiate both numerator and denominator to get the limit.
    After differentiation we get
    => limit as x minus greater than 0 of fraction numerator sec squared open parentheses x close parentheses minus cos open parentheses x close parentheses over denominator 2 x end fraction
    Again after putting the value of limit we are getting open parentheses 0 over 0 close parentheses space f o r m
    Step3:  Again Differentiating
    => limit as x minus greater than 0 of fraction numerator 2 sec open parentheses x close parentheses left parenthesis sec open parentheses x close parentheses tan open parentheses x close parentheses right parenthesis minus left parenthesis negative sin open parentheses x close parentheses right parenthesis over denominator 2 end fraction
    => limit as x minus greater than 0 of fraction numerator 2 sec squared open parentheses x close parentheses tan open parentheses x close parentheses plus sin open parentheses x close parentheses over denominator 2 end fraction
    We will put the value of limit in both the numerator and denominator
    by putting straight x equals 0 in both numerator and denominator we get,
    => limit as x minus greater than 0 of fraction numerator 2 cross times left parenthesis 1 right parenthesis cross times 0 plus 0 over denominator 2 end fraction
    =>0
    So, the value of the limit is 0.

    Related Questions to study

    General
    Maths-

    L t subscript left parenthesis x rightwards arrow 8 right parenthesis invisible function application left parenthesis √ left parenthesis 1 plus √ left parenthesis 1 plus x right parenthesis right parenthesis minus 2 right parenthesis divided by left parenthesis x minus 8 right parenthesis equals

    L t subscript left parenthesis x rightwards arrow 8 right parenthesis invisible function application left parenthesis √ left parenthesis 1 plus √ left parenthesis 1 plus x right parenthesis right parenthesis minus 2 right parenthesis divided by left parenthesis x minus 8 right parenthesis equals

    Maths-General
    General
    Maths-

    If a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1 then stack b with ‾ on top equals

    For such questions, we should know how to find the dot product and cross product. Dot product of two vectors is always a scalar quantity. The cross product of two vectors is a vector quantity.

    If a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1 then stack b with ‾ on top equals

    Maths-General

    For such questions, we should know how to find the dot product and cross product. Dot product of two vectors is always a scalar quantity. The cross product of two vectors is a vector quantity.

    General
    Maths-

    If a with ‾ on top comma b with ‾ on top comma c with ‾ on top are non coplanar vectors then the roots of equation open square brackets table attributes columnalign left end attributes row cell stack b with ‾ on top cross times stack c with ‾ on top end cell cell stack c with ‾ on top cross times stack a with ‾ on top end cell cell stack a with ‾ on top cross times stack b with ‾ on top end cell end table close square brackets x to the power of 2 end exponent plus open square brackets table attributes columnalign left end attributes row cell stack a with ‾ on top plus stack b with ‾ on top end cell cell stack b with ‾ on top plus stack c with ‾ on top end cell cell stack c with ‾ on top plus stack a with ‾ on top end cell end table close square brackets x plus open square brackets table attributes columnalign left end attributes row cell stack b with ‾ on top minus stack c with ‾ on top end cell cell stack c with ‾ on top minus stack a with ‾ on top end cell cell stack a with ‾ on top minus stack b with ‾ on top end cell end table close square brackets plus 1 equals 0

    If a with ‾ on top comma b with ‾ on top comma c with ‾ on top are non coplanar vectors then the roots of equation open square brackets table attributes columnalign left end attributes row cell stack b with ‾ on top cross times stack c with ‾ on top end cell cell stack c with ‾ on top cross times stack a with ‾ on top end cell cell stack a with ‾ on top cross times stack b with ‾ on top end cell end table close square brackets x to the power of 2 end exponent plus open square brackets table attributes columnalign left end attributes row cell stack a with ‾ on top plus stack b with ‾ on top end cell cell stack b with ‾ on top plus stack c with ‾ on top end cell cell stack c with ‾ on top plus stack a with ‾ on top end cell end table close square brackets x plus open square brackets table attributes columnalign left end attributes row cell stack b with ‾ on top minus stack c with ‾ on top end cell cell stack c with ‾ on top minus stack a with ‾ on top end cell cell stack a with ‾ on top minus stack b with ‾ on top end cell end table close square brackets plus 1 equals 0

    Maths-General
    parallel
    General
    Maths-

    The point of intersection of the plane r with rightwards arrow on top times left parenthesis 3 i with ˆ on top minus 5 j with ˆ on top plus 2 k with ˆ on top right parenthesis equals 6 will the stright line passing through the origin and perpendicular to the plane 2 x minus y minus z equals 4 is

    The point of intersection of the plane r with rightwards arrow on top times left parenthesis 3 i with ˆ on top minus 5 j with ˆ on top plus 2 k with ˆ on top right parenthesis equals 6 will the stright line passing through the origin and perpendicular to the plane 2 x minus y minus z equals 4 is

    Maths-General
    General
    Maths-

    The position vector of the centre of the circle vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with rightwards arrow on top right parenthesis equals 3 square root of 3

    The position vector of the centre of the circle vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with rightwards arrow on top right parenthesis equals 3 square root of 3

    Maths-General
    General
    Maths-

    The locus of midpoints of chords of  which subtend a right angle  at the centre is

    The locus of midpoints of chords of  which subtend a right angle  at the centre is

    Maths-General
    parallel
    General
    Maths-

    𝐓𝐡𝐞𝐫𝐞 𝐚𝐫𝐞 𝐭𝐰𝐨 𝐔𝐫𝐧𝐬. 𝐔𝐫𝐧 𝐀 𝐡𝐚𝐬 𝟑 𝐝𝐢𝐬𝐭𝐢𝐧𝐜𝐭 𝐫𝐞𝐝 𝐛𝐚𝐥𝐥𝐬 𝐚𝐧𝐝 𝐮𝐫𝐧 𝐁 𝐡𝐚𝐬 𝟗 𝐝𝐢𝐬𝐭𝐢𝐧𝐜𝐭 𝐛𝐥𝐮𝐞 𝐛𝐚𝐥𝐥𝐬. 𝐅𝐫𝐨𝐦 𝐞𝐚𝐜𝐡 𝐮𝐫𝐧 𝐭𝐰𝐨 𝐛𝐚𝐥𝐥𝐬 𝐚𝐫𝐞 𝐭𝐚𝐤𝐞𝐧 𝐨𝐮𝐭 𝐚𝐭𝐫𝐚𝐧𝐝𝐨𝐦 𝐚𝐧𝐝 𝐭𝐡𝐞𝐧 𝐭𝐫𝐚𝐧𝐬𝐟𝐞𝐫𝐫𝐞𝐝 𝐭𝐨 𝐭𝐡𝐞 𝐨𝐭𝐡𝐞𝐫. 𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝐭𝐡𝐢𝐬 𝐜𝐚𝐧 𝐛𝐞 𝐝𝐨𝐧𝐞 𝐢𝐬

    𝐓𝐡𝐞𝐫𝐞 𝐚𝐫𝐞 𝐭𝐰𝐨 𝐔𝐫𝐧𝐬. 𝐔𝐫𝐧 𝐀 𝐡𝐚𝐬 𝟑 𝐝𝐢𝐬𝐭𝐢𝐧𝐜𝐭 𝐫𝐞𝐝 𝐛𝐚𝐥𝐥𝐬 𝐚𝐧𝐝 𝐮𝐫𝐧 𝐁 𝐡𝐚𝐬 𝟗 𝐝𝐢𝐬𝐭𝐢𝐧𝐜𝐭 𝐛𝐥𝐮𝐞 𝐛𝐚𝐥𝐥𝐬. 𝐅𝐫𝐨𝐦 𝐞𝐚𝐜𝐡 𝐮𝐫𝐧 𝐭𝐰𝐨 𝐛𝐚𝐥𝐥𝐬 𝐚𝐫𝐞 𝐭𝐚𝐤𝐞𝐧 𝐨𝐮𝐭 𝐚𝐭𝐫𝐚𝐧𝐝𝐨𝐦 𝐚𝐧𝐝 𝐭𝐡𝐞𝐧 𝐭𝐫𝐚𝐧𝐬𝐟𝐞𝐫𝐫𝐞𝐝 𝐭𝐨 𝐭𝐡𝐞 𝐨𝐭𝐡𝐞𝐫. 𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝐭𝐡𝐢𝐬 𝐜𝐚𝐧 𝐛𝐞 𝐝𝐨𝐧𝐞 𝐢𝐬

    Maths-General
    General
    Maths-

    𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐩𝐞𝐫𝐦𝐮𝐭𝐚𝐭𝐢𝐨𝐧𝐬 𝐟𝐫𝐨𝐦 𝐭𝐡𝐞 𝐥𝐞𝐭𝐭𝐞𝐫𝐬 𝐀 𝐭𝐨 𝐆 𝐬𝐨 𝐭𝐡𝐚𝐭 𝐧𝐞𝐢𝐭𝐡𝐞𝐫 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐁𝐄𝐆 𝐧𝐨𝐫 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐂𝐀𝐃 𝐚𝐩𝐩𝐞𝐚𝐫𝐬 𝐢𝐬

    𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐩𝐞𝐫𝐦𝐮𝐭𝐚𝐭𝐢𝐨𝐧𝐬 𝐟𝐫𝐨𝐦 𝐭𝐡𝐞 𝐥𝐞𝐭𝐭𝐞𝐫𝐬 𝐀 𝐭𝐨 𝐆 𝐬𝐨 𝐭𝐡𝐚𝐭 𝐧𝐞𝐢𝐭𝐡𝐞𝐫 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐁𝐄𝐆 𝐧𝐨𝐫 𝐭𝐡𝐞 𝐬𝐞𝐭 𝐂𝐀𝐃 𝐚𝐩𝐩𝐞𝐚𝐫𝐬 𝐢𝐬

    Maths-General
    General
    Maths-

    L t subscript left parenthesis x rightwards arrow 0 right parenthesis invisible function application x divided by left parenthesis √ left parenthesis x plus 4 right parenthesis minus 2 right parenthesis equals

    L t subscript left parenthesis x rightwards arrow 0 right parenthesis invisible function application x divided by left parenthesis √ left parenthesis x plus 4 right parenthesis minus 2 right parenthesis equals

    Maths-General
    parallel
    General
    Maths-

    A unit vector stack a with rightwards arrow on top in the plane of b with rightwards arrow on top equals 2 i with ˆ on top plus j with ˆ on top & c with rightwards arrow on top equals i with ˆ on top minus j with ˆ on top plus k with ˆ on top is such that stack a with rightwards arrow on top stack b with rightwards arrow on top equals stack a with rightwards arrow on top stack b with rightwards arrow on top where d with rightwards arrow on top equals j with ˆ on top plus 2 k with ˆ on top is

    A unit vector stack a with rightwards arrow on top in the plane of b with rightwards arrow on top equals 2 i with ˆ on top plus j with ˆ on top & c with rightwards arrow on top equals i with ˆ on top minus j with ˆ on top plus k with ˆ on top is such that stack a with rightwards arrow on top stack b with rightwards arrow on top equals stack a with rightwards arrow on top stack b with rightwards arrow on top where d with rightwards arrow on top equals j with ˆ on top plus 2 k with ˆ on top is

    Maths-General
    General
    Maths-

    If a with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i with ˆ on top plus j with ˆ on top minus k with ˆ on top. Then altitude of the parallel piped formed by the vectors stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top having base formed by stack b with rightwards arrow on top & stack c with rightwards arrow on top is ( stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top and a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank, c with rightwards arrow on top to the power of blank are reciprocal system of vectors)

    If a with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i with ˆ on top plus j with ˆ on top minus k with ˆ on top. Then altitude of the parallel piped formed by the vectors stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top having base formed by stack b with rightwards arrow on top & stack c with rightwards arrow on top is ( stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top and a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank, c with rightwards arrow on top to the power of blank are reciprocal system of vectors)

    Maths-General
    General
    Maths-

    The vector i with minus on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times i with minus on top right parenthesis right square bracket plus j with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times j with ‾ on top right square bracket plus k with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times k with ‾ on top right square bracket equals

    The vector i with minus on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times i with minus on top right parenthesis right square bracket plus j with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times j with ‾ on top right square bracket plus k with ‾ on top cross times left square bracket left parenthesis a with ‾ on top cross times b with ‾ on top right parenthesis cross times k with ‾ on top right square bracket equals

    Maths-General
    parallel
    General
    Maths-

    O A B C is a tetrahedron in which O is the origin and position vector of points A,B,C  are i with ˆ on top plus 2 j plus 3 k with ˆ on top comma 2 i plus a j plus k with ˆ on top and i with ˆ on top plus 3 j with ˆ on top plus 2 k with ˆ on top respectively. A value of a for which shortest distance between O A and B C is square root of fraction numerator 3 over denominator 2 end fraction end root

    O A B C is a tetrahedron in which O is the origin and position vector of points A,B,C  are i with ˆ on top plus 2 j plus 3 k with ˆ on top comma 2 i plus a j plus k with ˆ on top and i with ˆ on top plus 3 j with ˆ on top plus 2 k with ˆ on top respectively. A value of a for which shortest distance between O A and B C is square root of fraction numerator 3 over denominator 2 end fraction end root

    Maths-General
    General
    Maths-

    𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝐭𝐡𝐞 𝐟𝐨𝐮𝐫 𝐟𝐚𝐜𝐞𝐬 𝐨𝐟 𝐚 𝐫𝐞𝐠𝐮𝐥𝐚𝐫 𝐭𝐞𝐭𝐫𝐚𝐡𝐞𝐝𝐫𝐨𝐧 𝐜𝐚𝐧 𝐛𝐞 𝐩𝐚𝐢𝐧𝐭𝐞𝐝 𝐰𝐢𝐭𝐡 𝐟𝐨𝐮𝐫 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐜𝐨𝐥𝐨𝐮𝐫𝐬 𝐢𝐬

    𝐓𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝐭𝐡𝐞 𝐟𝐨𝐮𝐫 𝐟𝐚𝐜𝐞𝐬 𝐨𝐟 𝐚 𝐫𝐞𝐠𝐮𝐥𝐚𝐫 𝐭𝐞𝐭𝐫𝐚𝐡𝐞𝐝𝐫𝐨𝐧 𝐜𝐚𝐧 𝐛𝐞 𝐩𝐚𝐢𝐧𝐭𝐞𝐝 𝐰𝐢𝐭𝐡 𝐟𝐨𝐮𝐫 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐜𝐨𝐥𝐨𝐮𝐫𝐬 𝐢𝐬

    Maths-General
    General
    Maths-

    T𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝟓 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥 𝐛𝐚𝐥𝐥𝐬 𝐜𝐚𝐧 𝐛𝐞 𝐤𝐞𝐩𝐭 𝐢𝐧 𝟏𝟎 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥 𝐛𝐨𝐱𝐞𝐬, 𝐢𝐟 𝐧𝐨𝐭 𝐦𝐨𝐫𝐞 𝐭𝐡𝐚𝐧 𝐨𝐧𝐞 𝐜𝐚𝐧 𝐠𝐨 𝐢𝐧𝐭𝐨 𝐚 𝐛𝐨𝐱, 𝐢𝐬

    T𝐡𝐞 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 𝐢𝐧 𝐰𝐡𝐢𝐜𝐡 𝟓 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥 𝐛𝐚𝐥𝐥𝐬 𝐜𝐚𝐧 𝐛𝐞 𝐤𝐞𝐩𝐭 𝐢𝐧 𝟏𝟎 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥 𝐛𝐨𝐱𝐞𝐬, 𝐢𝐟 𝐧𝐨𝐭 𝐦𝐨𝐫𝐞 𝐭𝐡𝐚𝐧 𝐨𝐧𝐞 𝐜𝐚𝐧 𝐠𝐨 𝐢𝐧𝐭𝐨 𝐚 𝐛𝐨𝐱, 𝐢𝐬

    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.