Final answer:
To evaluate the limit limx->1 f(x)-f(1)/(x-1), we simplify the expression by finding the difference f(x)-f(1) and then factorizing the numerator. Finally, substitute x=1 to find the limit.
Step-by-step explanation:
To evaluate the limit limx→1f(x)-f(1)/(x-1), we first need to find the expression for f(x)-f(1). Substituting x=1 into the function f(x)=x^2-16x, we get f(1)=1^2-16(1)=-15.
So, f(x)-f(1)=x^2-16x-(-15)=x^2-16x+15.
Now, we substitute this expression in the limit expression: limx→1(x^2-16x+15)/(x-1).
To evaluate this limit, we can further simplify the expression by factoring the numerator: (x-1)(x-15)/(x-1).
Notice that (x-1) cancels out in the numerator and denominator. So, we are left with limx→1(x-15)=1-15=-14.