Use the linear approximation to prove the following version of L'Hospital's Rule:
Let f(c)=g(c)=0 and g'(c) does not = 0. If f and g are differentable at x=c, then the limit as x approaches c of f(x)/g(x)=f'(c)/g'(c).
Where do I even begin? I know how to do linear approximations and that the equation is L(x)=f(a)+f'(a)(x-a), but how do I apply that to this version of L'Hospital's Rule?
Let f(c)=g(c)=0 and g'(c) does not = 0. If f and g are differentable at x=c, then the limit as x approaches c of f(x)/g(x)=f'(c)/g'(c).
Where do I even begin? I know how to do linear approximations and that the equation is L(x)=f(a)+f'(a)(x-a), but how do I apply that to this version of L'Hospital's Rule?