Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x minus 3 over denominator square root of open vertical bar x squared minus 9 close vertical bar end root end fraction

  1. 1
  2. 3
  3. 0
  4. 9

Hint:

In this question, space open vertical bar x squared minus 9 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x squared minus 9 end cell cell comma space i f space x greater or equal than 3 end cell row cell x squared minus 9 end cell cell comma space i f space x less than 3 end cell end table closewe will consider x squared minus 9 as x=3. Then we will evaluate and later put the value of x.

The correct answer is: 0


    space space space limit as x rightwards arrow 3 of space fraction numerator x minus 3 over denominator square root of open vertical bar x squared minus 9 close vertical bar end root end fraction
w h e r e comma space open vertical bar x squared minus 9 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x squared minus 9 end cell cell comma space i f space x greater or equal than 3 end cell row cell x squared minus 9 end cell cell comma space i f space x less than 3 end cell end table close
equals limit as x rightwards arrow 3 of space fraction numerator x minus 3 over denominator square root of x squared minus 9 end root end fraction
equals limit as x rightwards arrow 3 of space fraction numerator square root of left parenthesis x minus 3 right parenthesis left parenthesis x minus 3 right parenthesis end root over denominator square root of open parentheses x plus 3 right parenthesis left parenthesis x minus 3 close parentheses end root end fraction
equals limit as x rightwards arrow 3 of space fraction numerator square root of x minus 3 end root over denominator square root of x plus 3 end root end fraction
equals fraction numerator square root of 3 minus 3 end root over denominator square root of 3 plus 3 end root end fraction
equals 0 over 6
equals 0

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    physics-

    A meter bridge is set up as shown in figure, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping - key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is

    A meter bridge is set up as shown in figure, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping - key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is

    physics-General
    General
    chemistry-

    The concentration of electrolyte required to coagulate a given amount of A s subscript 2 S subscript 3 sol is minimum in the case of

    The concentration of electrolyte required to coagulate a given amount of A s subscript 2 S subscript 3 sol is minimum in the case of

    chemistry-General
    General
    physics-

    To verify ohm’s law, a student is provided with a test resistor RT , a high resistance R1 , a small resistance R2 , two identical galvanometers G1 and G2 , and a variable voltage source V. The correct circuit to carry out the experiment is

    To verify ohm’s law, a student is provided with a test resistor RT , a high resistance R1 , a small resistance R2 , two identical galvanometers G1 and G2 , and a variable voltage source V. The correct circuit to carry out the experiment is

    physics-General
    General
    physics-

    If by mistake, voltmeter is connected in series with the resistance then i-v curve expected is (Here i = reading of ammter ,v=reading of voltmeter)

    If by mistake, voltmeter is connected in series with the resistance then i-v curve expected is (Here i = reading of ammter ,v=reading of voltmeter)

    physics-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 0 to the power of x plus 2 end exponent plus 4 end subscript fraction numerator 3 to the power of x plus 1 end exponent plus 4 over denominator 3 to the power of x plus 2 end exponent end fraction

    Lt subscript x not stretchy rightwards arrow 0 to the power of x plus 2 end exponent plus 4 end subscript fraction numerator 3 to the power of x plus 1 end exponent plus 4 over denominator 3 to the power of x plus 2 end exponent end fraction

    maths-General
    General
    maths-

    open Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses

    open Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator sin to the power of negative 1 end exponent space x over denominator x end fraction close parentheses

    maths-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 2 x over denominator tan to the power of negative 1 end exponent space x end fraction

    Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 2 x over denominator tan to the power of negative 1 end exponent space x end fraction

    maths-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction

    Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction

    maths-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript space 2 over x log space left parenthesis 1 plus x right parenthesis

    Lt subscript x not stretchy rightwards arrow 0 end subscript space 2 over x log space left parenthesis 1 plus x right parenthesis

    maths-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 0 end subscript open parentheses 1 plus fraction numerator 2 x over denominator 3 end fraction close parentheses to the power of 1 over x end exponent

    Lt subscript x not stretchy rightwards arrow 0 end subscript open parentheses 1 plus fraction numerator 2 x over denominator 3 end fraction close parentheses to the power of 1 over x end exponent

    maths-General
    General
    maths-

    stack L t with x not stretchy rightwards arrow negative 1.5 below cos to the power of negative 1 end exponent space open parentheses fraction numerator x plus 3 over denominator 3 end fraction close parentheses

    stack L t with x not stretchy rightwards arrow negative 1.5 below cos to the power of negative 1 end exponent space open parentheses fraction numerator x plus 3 over denominator 3 end fraction close parentheses

    maths-General
    General
    maths-

    Lt subscript x not stretchy rightwards arrow 2 end subscript space 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

    Lt subscript x not stretchy rightwards arrow 2 end subscript space 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

    maths-General
    General
    maths-

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

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

    maths-General
    General
    maths-

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x to the power of 0 minus sin space 3 x to the power of 8 over denominator x cubed end fraction

    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x to the power of 0 minus sin space 3 x to the power of 8 over denominator x cubed end fraction

    maths-General
    General
    chemistry-

    Gas masks containing activated charcoal to remove poisonous gases from atmosphere acts on the principle of :

    Gas masks containing activated charcoal to remove poisonous gases from atmosphere acts on the principle of :

    chemistry-General