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Asked by sarveshvibrantacademy | 05 May, 2019, 15:44: PM
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L e t space L equals limit as x rightwards arrow 0 of open parentheses 1 plus e to the power of negative 1 over x squared end exponent tan to the power of negative 1 end exponent open parentheses 1 over x squared close parentheses plus x e to the power of negative 1 over x squared end exponent sin open parentheses 1 over x to the power of 4 close parentheses close parentheses to the power of e to the power of 1 over x squared end exponent end exponent space i s o f space t h e space f o r m space 1 to the power of infinity space w h e n space x rightwards arrow 0 rightwards double arrow L equals e to the power of limit as x rightwards arrow 0 of space open parentheses e to the power of 1 over x squared end exponent close parentheses space space open parentheses 1 plus e to the power of negative 1 over x squared end exponent tan to the power of negative 1 end exponent open parentheses 1 over x squared close parentheses plus x e to the power of negative 1 over x squared end exponent sin open parentheses 1 over x to the power of 4 close parentheses minus 1 close parentheses end exponent rightwards double arrow L equals e to the power of limit as x rightwards arrow 0 of space open parentheses e to the power of 1 over x squared end exponent close parentheses space space open parentheses e to the power of negative 1 over x squared end exponent tan to the power of negative 1 end exponent open parentheses 1 over x squared close parentheses plus x e to the power of negative 1 over x squared end exponent sin open parentheses 1 over x to the power of 4 close parentheses close parentheses end exponent rightwards double arrow L equals e to the power of limit as x rightwards arrow 0 of space space space open parentheses tan to the power of negative 1 end exponent open parentheses 1 over x squared close parentheses plus x space sin open parentheses 1 over x to the power of 4 close parentheses close parentheses end exponent rightwards double arrow L equals e to the power of space open parentheses tan to the power of negative 1 end exponent open parentheses 1 over 0 close parentheses plus 0 space sin open parentheses 1 over 0 close parentheses close parentheses end exponent rightwards double arrow L equals e to the power of space open parentheses tan to the power of negative 1 end exponent open parentheses infinity close parentheses close parentheses end exponent rightwards double arrow L equals e to the power of straight pi divided by 2 end exponent H e n c e comma space limit as x rightwards arrow 0 of open parentheses 1 plus e to the power of negative 1 over x squared end exponent tan to the power of negative 1 end exponent open parentheses 1 over x squared close parentheses plus x e to the power of negative 1 over x squared end exponent sin open parentheses 1 over x to the power of 4 close parentheses close parentheses to the power of e to the power of 1 over x squared end exponent end exponent space equals e to the power of straight pi divided by 2 end exponent
Answered by Renu Varma | 06 May, 2019, 10:49: AM

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