Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets x to the power of 6 plus square root of x squared plus 1292 end root close square brackets

  1. 1
  2. 2
  3. 0
  4. 6

hintHint:

Finding limits for the vast majority of points for a given function is as simple as substituting the number that x approaches into the function. 
In this question, we have to find value of Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets x to the power of 6 plus square root of x squared plus 1292 end root close square brackets.

The correct answer is: 2


    Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets x to the power of 6 plus square root of x squared plus 1292 end root close square brackets
    On substituting, We get
    Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 2 to the power of 6 plus square root of 2 squared plus 1292 end root close square brackets
Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 2 to the power of 6 plus square root of 1296 close square brackets       (  square root of 1296 space end root equals space 36 squared)
    Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 2 to the power of 6 plus space 36 close square brackets                ( 2 to the power of 6 equals 64)
    Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 100 close square brackets space equals Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 10 squared close square brackets space equals space 2 space Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 10 close square brackets
    ( We know that ,log10(10) =1)
    so,space 2 space Lt subscript x not stretchy rightwards arrow 2 end subscript log subscript 10 space open square brackets 10 close square brackets space equals 2

    Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b to the power of x= n, in which case one writes x = log subscript b to the power of blank to the power of blank end exponent end subscript n.

    Related Questions to study

    General
    physics-

    The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used

    The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used

    physics-General
    General
    physics-

    The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v

    The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v

    physics-General
    General
    physics-

    When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that

    When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that

    physics-General
    parallel
    General
    Maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 minus cos space x over denominator x squared end fraction

    We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 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 0 end subscript fraction numerator 1 minus cos space x over denominator x squared end fraction

    Maths-General

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

    General
    Maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x minus sin space 3 x to the power of blank over denominator x cubed end fraction

    We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 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 0 end subscript fraction numerator 3 sin space x minus sin space 3 x to the power of blank over denominator x cubed end fraction

    Maths-General

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

    General
    maths-

    The value of integral subscript 0 superscript 4   e to the power of x d x on using simpson's 3rd rule by taking h=1 is [Given open straight e equals 2.72 comma straight e squared equals 7.39 comma straight e to the power of 8 equals 20.09 comma straight e to the power of 4 equals 54.60 close square brackets

    The value of integral subscript 0 superscript 4   e to the power of x d x on using simpson's 3rd rule by taking h=1 is [Given open straight e equals 2.72 comma straight e squared equals 7.39 comma straight e to the power of 8 equals 20.09 comma straight e to the power of 4 equals 54.60 close square brackets

    maths-General
    parallel
    General
    physics-

    Which of the following statement is correct

    Which of the following statement is correct

    physics-General
    General
    Maths-

    α is a solution of the equation z to the power of n equals left parenthesis z plus 1 right parenthesis n where n greater or equal than2, n element of N. Then the probability that alphalies on the real axis is

    α is a solution of the equation z to the power of n equals left parenthesis z plus 1 right parenthesis n where n greater or equal than2, n element of N. Then the probability that alphalies on the real axis is

    Maths-General
    General
    maths-

    Tan invisible function application 25 to the power of ring operator Tan invisible function application 31 to the power of ring operator plus Tan invisible function application 31 to the power of ring operator Tan invisible function application 34 to the power of ring operator plus Tan invisible function application 34 to the power of ring operator Tan invisible function application 25 to the power of ring operator

    Tan invisible function application 25 to the power of ring operator Tan invisible function application 31 to the power of ring operator plus Tan invisible function application 31 to the power of ring operator Tan invisible function application 34 to the power of ring operator plus Tan invisible function application 34 to the power of ring operator Tan invisible function application 25 to the power of ring operator

    maths-General
    parallel
    General
    maths-

    If Tan invisible function application 8 A minus Tan invisible function application 5 A minus Tan invisible function application 3 A equals K Tan invisible function application 8 A Tan invisible function application 5 A times Tan invisible function application 3 A then K=

    If Tan invisible function application 8 A minus Tan invisible function application 5 A minus Tan invisible function application 3 A equals K Tan invisible function application 8 A Tan invisible function application 5 A times Tan invisible function application 3 A then K=

    maths-General
    General
    maths-

    cos invisible function application 35 to the power of ring operator plus Cos invisible function application 85 to the power of ring operator plus Cos invisible function application 155 to the power of ring operator equals

    cos invisible function application 35 to the power of ring operator plus Cos invisible function application 85 to the power of ring operator plus Cos invisible function application 155 to the power of ring operator equals

    maths-General
    General
    maths-

    Tan invisible function application 100 to the power of ring operator plus Tan invisible function application 125 to the power of ring operator plus Tan invisible function application 100 to the power of ring operator Tan invisible function application 125 to the power of ring operator equals

    Tan invisible function application 100 to the power of ring operator plus Tan invisible function application 125 to the power of ring operator plus Tan invisible function application 100 to the power of ring operator Tan invisible function application 125 to the power of ring operator equals

    maths-General
    parallel
    General
    maths-

    If Tan invisible function application 69 to the power of ring operator plus Tan invisible function application 66 to the power of ring operator minus Tan invisible function application 69 to the power of ring operator. Tan invisible function application 66 to the power of ring operator equals 2 k then k=

    If Tan invisible function application 69 to the power of ring operator plus Tan invisible function application 66 to the power of ring operator minus Tan invisible function application 69 to the power of ring operator. Tan invisible function application 66 to the power of ring operator equals 2 k then k=

    maths-General
    General
    physics-

    Three right angled prisms of refractive indices n subscript 1 end subscript comma n subscript 2 end subscript and n subscript 3 end subscript are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then

    Three right angled prisms of refractive indices n subscript 1 end subscript comma n subscript 2 end subscript and n subscript 3 end subscript are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then

    physics-General
    General
    physics-

    The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be

    The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be

    physics-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.