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Asked by sarveshvibrantacademy | 29 May, 2019, 12:01: AM
answered-by-expert Expert Answer
L e t space L equals limit as x rightwards arrow 0 to the power of plus of space x to the power of open parentheses x to the power of x minus 1 close parentheses end exponent
rightwards double arrow ln space L equals ln open parentheses limit as x rightwards arrow 0 to the power of plus of space x to the power of open parentheses x to the power of x minus 1 close parentheses end exponent close parentheses
N o w comma space ln open parentheses limit as x rightwards arrow 0 to the power of plus of space x to the power of open parentheses x to the power of x minus 1 close parentheses end exponent close parentheses equals limit as x rightwards arrow 0 to the power of plus of space ln open parentheses x to the power of open parentheses x to the power of x minus 1 close parentheses end exponent close parentheses
space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of space open parentheses x to the power of x minus 1 close parentheses space ln open parentheses x close parentheses
space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of space open parentheses x to the power of x minus 1 close parentheses space limit as x rightwards arrow 0 to the power of plus of space ln open parentheses x close parentheses
space space space space space space space space equals space minus infinity
rightwards double arrow ln space L equals negative infinity
rightwards double arrow L equals e to the power of negative infinity end exponent equals 0
H e n c e comma space limit as x rightwards arrow 0 to the power of plus of space x to the power of open parentheses x to the power of x minus 1 close parentheses end exponent equals 0
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