1.

Find the derivative of the following functions 'ab initio', that is, using the definition.s^2-bs+5

Answer»

Solution :LET `y=s^2-bs+5`
Then
`(dy)/(DS)=lim_(hto0)((s+H)^2-b(s+h)+5-(s^2-bs-5))/h`
`=lim_(hto0)((s^2+2hs+h^2-bs-bh+5-s^2+bs-5))/h`
`=lim_(hto0)(2hs-bh+h^2)/h`
`=lim_(hto0){2s-b+h}=2s-b`


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