(a) Show that the definition of the derivative apoilied to the function (x) -3% at x = 0 gives (0) - m For x = 0. F(x+5)-5(x) h & FOD 0.1 (b) Use a calculator to evaluate the difference quotient 0.001 0.00001 10+h 15 ** (c) From your answers to part (b), does the limit exist? O Yes, the limit exists. No, the limit does not exist. Does the derivative of f(x)-tx-exist? for the following values of h: 0.1, 0.001, and 0.00001. (Hint: Enter the calculation into your calculator with h replaced by 0.1, and then change the value of ihn by inserting zeros. Round your answers to three decimal O yes, the derivative exists at x-0. O No, the derivative does not exist at x-Q. (d) Graph f(x)=√x on the window (-3, 3) by (-3, 3). Do you see why the slope at x = 0 does not exist? 1 + 7