Find the function? The following limits represent the slope of a curve y = f(x) at the point (a, f(a)). Determine a function f and a number a; then, calculate the limit. 1 1 lim x+13 x?2 x?2

SOLUTION STEP 1 Given is the slope of the curve y=f(x) Thus it is the derivative of the function f(x). 1 1 ie,f(x) = lim x+13 x2 x2 Thus comparing with the definition of the derivative f(x)f(a) f(x) = lim xa xa Thus we can find that f(x) = 1 and a = 2 x+1...