Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x where a,b,c are real and non-zero=

  1. left parenthesis a b c right parenthesis
  2. left parenthesis a b c right parenthesis to the power of 1 third end exponent
  3. left parenthesis a b c right parenthesis to the power of 1 over x end exponent
  4. straight infinity

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 square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x.

The correct answer is: left parenthesis a b c right parenthesis to the power of 1 third end exponent


    Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x
    Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets fraction numerator a to the power of 1 over x end exponent plus b to the power of 1 over x end exponent plus c to the power of 1 over x end exponent over denominator 3 end fraction close square brackets to the power of x space equals space open square brackets fraction numerator a to the power of 1 over infinity end exponent plus b to the power of 1 over infinity end exponent plus c to the power of 1 over infinity end exponent over denominator 3 end fraction close square brackets to the power of infinity equals 1 to the power of infinity   where a,b,c are real and non-zero
    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.
    Error converting from MathML to accessible text.

    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.

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