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Continuity And Differentiability

Question
CBSEENMA12035397
Wired Faculty App

If space straight y equals 500 space straight e to the power of 7 straight x end exponent plus 600 space straight e to the power of negative 7 straight x end exponent comma space show space that space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 49 space straight y.

Solution
space space space space space space space space space space space space space straight y equals 500 space straight e to the power of 7 straight x end exponent plus 600 space straight e to the power of negative 7 straight x end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis space space space space space space space dy over dx equals 3500 space straight e to the power of 7 straight x end exponent minus 4200 space straight e to the power of negative 7 straight x end exponent space space space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 24500 space straight e to the power of 7 straight x end exponent plus 29400 space straight e to the power of negative 7 straight x end exponent rightwards double arrow space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 49 left parenthesis 500 space straight e to the power of 7 straight x end exponent plus 600 space straight e to the power of negative 7 straight x end exponent right parenthesis rightwards double arrow space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 49 space straight y space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because space of space 1 right square bracket

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