JEE Class main Answered

solve

Asked by sarveshvibrantacademy | 29 May, 2019, 12:01: AM

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

Answered by Renu Varma | 29 May, 2019, 10:23: AM

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