Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 1 end exponent

  1. e to the power of 6
  2. e to the power of 4
  3. e
  4. e cubed

hintHint:

The initial form for the limit is indeterminate 1 to the power of infinity to the power of infinity  So, use the formula. In this question, we have to find value of Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 1 end exponent.

The correct answer is: e cubed


    Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 1 end exponent
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator 1 plus begin display style 6 over x end style over denominator 1 plus begin display style 1 over x end style end fraction close parentheses to the power of x plus 1 end exponent space space space space left parenthesis W e space c a n space w r i t e space space left parenthesis x plus a right parenthesis space equals space x left parenthesis 1 plus a over x right parenthesis. space space space right parenthesis
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator 1 plus begin display style 6 over x end style over denominator 1 plus begin display style 1 over x end style end fraction close parentheses to the power of x plus 1 end exponent equals space space open parentheses fraction numerator 1 plus begin display style a over infinity end style over denominator 1 plus begin display style b over infinity end style end fraction close parentheses to the power of infinity space equals 1 to the power of infinity
    bold 1 to the power of bold infinity bold space bold italic f bold italic o bold italic r bold italic m this is known as an indeterminate form, because it is unknown. One to the power infinity is unknown because infinity itself is endless. Take a look at some examples of indeterminate forms. To solve this limit we will use the following formula -
    Error converting from MathML to accessible text.
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus 6 over denominator x plus 1 end fraction close parentheses to the power of x plus 1 end exponent equals e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow straight infinity end subscript space stretchy left parenthesis fraction numerator straight x plus 6 over denominator straight x plus 1 end fraction minus 1 stretchy right parenthesis. left parenthesis straight x plus 1 right parenthesis space right parenthesis end exponent
e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow straight infinity end subscript space stretchy left parenthesis fraction numerator 6 minus 1 over denominator straight x plus 1 end fraction stretchy right parenthesis. left parenthesis straight x plus 1 right parenthesis space right parenthesis end exponent space equals e to the power of left parenthesis space Lt subscript straight x not stretchy rightwards arrow infinity end subscript space e to the power of left parenthesis 5 right parenthesis end exponent end exponent space equals space e to the power of 5

    The basic problem of this indeterminate form is to know from where f not stretchy left parenthesis x not stretchy right parenthesis tends to one (right or left) and what function reaches its limit more rapidly.

    Related Questions to study

    General
    Maths-

    text  Lt  end text subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 3 end exponent equals

    text  Lt  end text subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses fraction numerator x plus 5 over denominator x plus 2 end fraction close parentheses to the power of x plus 3 end exponent equals

    Maths-General
    General
    Maths-

    Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals

    Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals

    Maths-General
    General
    maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals

    maths-General
    parallel
    General
    Maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals

    Maths-General
    General
    Maths-

    text  If  end text a greater than 0 text  and  end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative 1 text , then  end text bold a equals

    text  If  end text a greater than 0 text  and  end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative 1 text , then  end text bold a equals

    Maths-General
    General
    Maths-

    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos space x right parenthesis minus b sin space x over denominator x cubed end fraction equals 1 text  then  end text straight a equals comma straight b equals

    L subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos space x right parenthesis minus b sin space x over denominator x cubed end fraction equals 1 text  then  end text straight a equals comma straight b equals

    Maths-General
    parallel
    General
    physics-

    The correct relation is.

    The correct relation is.

    physics-General
    General
    physics-

    A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
    (S.T. of water == fraction numerator 75 text  dyne  end text over denominator cm end fraction straight g equals 1000 straight m over straight s squared times)

    A vessel whose bottom has round holes with diameter of 0.1 mm is filled with water. The maximum height to which the water can be filled without leakage is
    (S.T. of water == fraction numerator 75 text  dyne  end text over denominator cm end fraction straight g equals 1000 straight m over straight s squared times)

    physics-General
    General
    Maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals

    Maths-General
    parallel
    General
    Maths-

    L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n open parentheses 1 cubed plus 2 cubed plus midline horizontal ellipsis times plus n cubed close parentheses squared over denominator open parentheses 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared close parentheses cubed end fraction equals

    L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n open parentheses 1 cubed plus 2 cubed plus midline horizontal ellipsis times plus n cubed close parentheses squared over denominator open parentheses 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared close parentheses cubed end fraction equals

    Maths-General
    General
    physics-

    A capillary tube at radius R  is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be

    A capillary tube at radius R  is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in the, capillary tube will now be

    physics-General
    General
    Maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator sin squared space x end fraction minus fraction numerator 1 over denominator sinh squared space x end fraction equals

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator sin squared space x end fraction minus fraction numerator 1 over denominator sinh squared space x end fraction equals

    Maths-General
    parallel
    General
    physics-

    If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be C r equals 1 space a n d space d e n s i t y space d equals 0.8 g m divided by c c right parenthesis

    If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surface tension of soap solution will be C r equals 1 space a n d space d e n s i t y space d equals 0.8 g m divided by c c right parenthesis

    physics-General
    General
    maths-

    The quadratic equation whose roots are I and m wherel equals lim for theta not stretchy rightwards arrow 0 of   open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of   open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses is

    The quadratic equation whose roots are I and m wherel equals lim for theta not stretchy rightwards arrow 0 of   open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of   open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses is

    maths-General
    General
    physics-

    Two bubbles A and B (A>B) are joined through a narrow tube than,

    Two bubbles A and B (A>B) are joined through a narrow tube than,

    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.