JEE Advanced2006MathematicsLimitsActual

For x>0, _ x 0 (( x)^ 1 / x + ( 1 x )^ x ) is

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Correct answer

C. 1

Step-by-step solution

Here, _ x 0 ( x)^ 1 / x + _ x 0 ( 1 x )^ x 0+ _ x 0 e^ ( 1 x )^ x array l _ x 0 ( x)^ 1 / x 0 as, (decimal) )^x 0 array e^ _ x 0 (1 / x) cosec x On applying L Hospital's Rule, we get e^ _ x 0 x (- 1 x^2 ) - cosec x x =e^ _ x 0 x x x =e^0=1

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