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If f(x)={{:(sinx","" "xnenpi", "ninI),...

If `f(x)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):}` and
`g(x)={{:(x^(2)+1","" "xne0", "2),(4","" "x=0),(5","" "x=2):}` then find `lim_(xto0) g{f(x)}`.

Text Solution

Verified by Experts

The correct Answer is:
1
`underset(xto0^(+))limg{f(x)}=g(f(0^(+)))=g((sin0^(+)))=g(0^(+))=(0)^(2)+1=1`
`underset(xto0^(-))limg{f(x)}=g(f(0^(-)))=g((sin0^(-)))=g(0^(-))=(0)^(2)+1=1`
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