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We have `underset(xtooo)limx^(n)f(x)=p` <br> `implies" "underset(xtooo)lim(x^(n+1)f(x))/(x)=p` <br> Using L'Hospital rule, we get <br> `underset(xtooo)lim((n+1)x^(n)f(x)^(n+1)f'(x))/(1)=p` <br> `implies" "(n+1)p+underset(xtooo)limx^(n+1)f'(x)=p` <br> `implies" "underset(xtooo)limx^(n+1)f'(x)=-np` <br> Further `underset(xtooo)lim(x^(n+2)f'(x))/(x)=-np` <br> Using L'Hospital rule, we get <br> `underset(xtooo)lim((n+2)x^(n+1)f'(x)+x^(n+2)f''(x))/(1)=-np` <br> `implies" "-np(n+2)+underset(xtooo)limx^(n+2)f''(x)=-np` <br> `implies" "underset(xtooo)limx^(n+2)f''(x)=up(1+n)`