Let the numerator of our function be called f (x), and let the denominator be called g(x). That is, f (x) = sin x and g(x)=x-7. Important: no quotient rule f(x) is a quotient, we will not be using the quotient rule in this problem. The quotient rule g(x) f(x) would find the derivative of h (x) = (2). However, we want to find the limit of h (x) as a approaches , not g(x) the derivative. Although h (x) = Local linearization Again, consider f (x) = sin x. Find the local linearization of f (x) at x = T. Call this tangent line equation Lf (x). I suggest the notation Lfas an abbreviation for the "L"inearization of function "f." Hints: You'll need to find f' (), and you'll need to find the y-value that corresponds to x = . Next, you can plug those pieces of information into the point-slope formula, Lf (x) - y = m (x x). Then, rearrange and simplify. L (x) = -x + T L (x) = -x - 2 Lf (x) = -2x +